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Removal of Power Line Interference and other Single Frequency Tones from Signals

MSc Thesis Report, Mälardalen University, Sweden 1

MSc ThesisMSc ThesisMSc ThesisMSc Thesis REPORT REPORT REPORT REPORT

LEVEL: 20 P, DLEVEL: 20 P, DLEVEL: 20 P, DLEVEL: 20 P, D----LEVELLEVELLEVELLEVEL

A report submitted to the Department of Computer Science and Electronics, Mälardalen University, A report submitted to the Department of Computer Science and Electronics, Mälardalen University, A report submitted to the Department of Computer Science and Electronics, Mälardalen University, A report submitted to the Department of Computer Science and Electronics, Mälardalen University,

in part fulin part fulin part fulin part fulfilment of the Degree of Master of Science in filment of the Degree of Master of Science in filment of the Degree of Master of Science in filment of the Degree of Master of Science in

Electronics with Biomedical EngineeringElectronics with Biomedical EngineeringElectronics with Biomedical EngineeringElectronics with Biomedical Engineering

By

Sheeraz Gul Tareen [email protected]

Tutor:

Mikael Ekström

Supervisor:

Prof. Rashid Baig

www.mdh.se

Department of Computer

Science and Electronics

08

[Removal of Power Line Interference and

other Single Frequency Tones from Signals]



Table of Contents

DEDICATION ___________________________________________________________ 7

ACKNOWLEDGEMENTS___________________________________________________ 8

ABSTRACT _____________________________________________________________ 9

1 CHAPTER-1 ________________________________________________________ 10

1.1 Problem Description ___________________________________________________ 10

1.2 The Purpose of Thesis __________________________________________________ 10

1.3 Report Layout ________________________________________________________ 11 1.3.1 Chapter-1 ________________________________________________________________ 11 1.3.2 Chapter-2 ________________________________________________________________ 11 1.3.3 Chapter-3 ________________________________________________________________ 11 1.3.4 Chapter-4 ________________________________________________________________ 11 1.3.5 Chapter-5 ________________________________________________________________ 11 1.3.6 Chapter-6 ________________________________________________________________ 12 1.3.7 Chapter-7 ________________________________________________________________ 12 1.3.8 Chapter-8 ________________________________________________________________ 12 1.3.9 References _______________________________________________________________ 12

2 CHAPTER-2 ________________________________________________________ 13

2.1 General Overview _____________________________________________________ 13 2.1.1 Heart Mechanism and Purpose of ECG Diagnosis ________________________________ 14

2.2 Background and Motivations.____________________________________________ 15

2.3 Thesis Specifications. __________________________________________________ 16

2.4 Thesis Aims and Objectives. _____________________________________________ 16

2.5 The Choice for MATLAB Software_________________________________________ 17

3 CHAPTER-3 ________________________________________________________ 18

3.1 Digital Signal Processing (DSP) ___________________________________________ 18

3.2 What are Filters_______________________________________________________ 18

3.3 What are Digital Filters? ________________________________________________ 19

3.4 Advantages of Digital Filters _____________________________________________ 19

3.5 Types of Digital Filters__________________________________________________ 20

3.6 Computational Properties and structure of Digital Filters Algorithm_____________ 21



3.7 DIGITAL FILTER ORDER, STEP-SIZE AND COEFFICIENTS ________________________ 22 3.7.1 Order of a Digital Filter _____________________________________________________ 22 3.7.2 Step-Size of a Digital Filter __________________________________________________ 23 3.7.3 Coefficient of the Digital Filter._______________________________________________ 23

4 CHAPTER-4 ________________________________________________________ 24

4.1 Introduction__________________________________________________________ 24

4.2 Explanation of Adaptive Filter ___________________________________________ 24

4.3 Adaptive Filters and Digital Signal Processing _______________________________ 25

4.4 Adaptive Filtering _____________________________________________________ 25

4.5 The General Structure of Adaptive Filters __________________________________ 26

4.6 Performance, Stability and Robustness of the Adaptive Algorithm ______________ 27

4.7 Convergence Criteria for Adaptive Algorithm _______________________________ 28

4.8 System Identification Configuration Using an Adaptive Filter __________________ 29

5 CHAPTER-5 ________________________________________________________ 31

5.1 Introduction__________________________________________________________ 31

5.2 Advantages of Filters and Adaptive Algorithm ______________________________ 31

5.3 Finite Impulse Response (FIR)____________________________________________ 32

5.4 FIR Filters Advantages and Disadvantages__________________________________ 33 5.4.1 Advantages: ______________________________________________________________ 33 5.4.2 Disadvantages:____________________________________________________________ 33

5.5 Comparison between FIR and IIR Filters ___________________________________ 33

5.6 Adaptive FIR Signal Processor____________________________________________ 34

6 CHAPTER-6 ________________________________________________________ 36

6.1 Adaptive Filter Algorithms ______________________________________________ 36

6.2 Introduction to LMS Algorithm___________________________________________ 36

6.3 Overview of the Structure and Operation of the LMS Algorithm ________________ 37

6.4 Design of an Adaptive Filter Algorithm ____________________________________ 38

6.5 Noise Cancellation_____________________________________________________ 39

6.6 Adaptive Noise Cancellation_____________________________________________ 41

6.7 Interference Cancellation by Adaptive Filtering _____________________________ 42

7 CHAPTER-7 ________________________________________________________ 44

7.1 Main Objective _______________________________________________________ 44

7.2 Design by DSP Technique _______________________________________________ 45



7.3 MATLAB Software Implementation _______________________________________ 45

7.4 Verification for Refinement of Signal by LMS _______________________________ 46 7.4.1 Removal of Power Line Interference (50 Hz) from ECG Signal by LMS Algorithm _______ 46 7.4.2 Removing of Harmonics and High Frequency Noise from Original ECG Signal __________ 51

7.5 Algorithm Implementation and Verification ________________________________ 53

8 CHAPTER-8 ________________________________________________________ 55

8.1 CONCLUSION AND FUTURE RESEARCH_____________________________________ 55 8.1.1 Conclusion _______________________________________________________________ 55 8.1.2 Suggestion for Future Work/Future Enhancement _______________________________ 56

9 APPENDIX A _______________________________________________________ 57

9.1 MATLAB CODE FOR ECG SIGNAL__________________________________________ 57

10 APPENDIX C _______________________________________________________ 61

10.1 MATLAB CODE FOR HARMONICS AND HIGH FREQUENCY NOISES FROM ECG SIGNAL

BY GENERAL NOTCH REJECTION FILTER _________________________________________ 61

11 REFERENCES _______________________________________________________ 65



List of Figures

FIGURE 21 – ECG signal with QRS complex _________________________________ 14

FIGURE 4.1 – Principle of an Adaptive Filter ________________________________ 26

FIGURE 4.2 – The general structure of an adaptive filter ______________________ 27

FIGURE 4.3 – System Identification Configuration for Adaptive Filter ____________ 29

FIGURE 5.1 – FINITE IMPULSE RESPONSE (FIR) FILTER STRUCTURE ____________________ 34

FIGURE 5.2– The Adaptive Signal Processor________________________________ 38

FIGURE 6.1 – LMS ADAPTIVE ALGORITHM _____________________________________ 37

FIGURE 6.2 – OUTLINE OF ADAPTIVE TRANSVERSAL FILTER __________________________ 39

FIGURE 6.3 – NOISE CANCELLATION EXAMPLE___________________________________ 40

FIGURE 6.4 – BLOCK DIAGRAM OF ADAPTIVE NOISE CANCELLER_______________________ 41

FIGURE 6.5 – INTERFERENCE CANCELLATION BY ADAPTIVE FILTERING____________________ 42



“Mind is not a vessel to be filled, but a fire to be kindled.”



DEDICATION

“I owe immense sense of gratitude to my beloved

Parents and family members who supported me financially as well

as morally, throughout my career. I also dedicate the thesis to my

university teachers who remained the source of encouragement

throughout.” Finally, I would like to thanks my sister ‘Nasreen

Akhtar’ who is educationist, friend ‘Noor’ who is doctor and all

other friends for their support and encouragement during the

critical time to finish this greatest task of my life.



ACKNOWLEDGEMENTS

I start with the name of Almighty Allah for providing me with the

unique opportunity to finalise this thesis.

It would not have been possible for me to complete this thesis

“Removal of Power Line Interference and other Single Frequency

Tones from Signals”,

except for the able guidance and constructive suggestions of my

thesis supervisor (Prof. Rashid Baig), thesis tutors (Mikael

Ekström). Their supervision and encouragement has made it

possible for me to complete this task, which is very important for

practical work.



ABSTRACT

Removal of Power Line Interference and other Single Frequency Tones from

Signals

With the latest advancements in electronics, several techniques are used for removal of

unwanted entities from signals especially that are implied in the most sophisticated

applications. The removal of power line interference from most sensitive medical

monitoring equipments can also be removed by implementing various useful

techniques. The power line interference (50/60 Hz) is the main source of noise in most

of bio-electric signals. The thesis report presents the removal of power line interference

and other single frequency tones from ECG signal using the advanced adaptive filtering

technique with LMS (least mean square) algorithm. The thesis is based on digital signal

processing (DSP) techniques with MATLAB package, with the emphases on design of

adaptive LMS algorithm. The adaptive interference removal technique can be used for

removal of power line interference in various potential applications such as recording

Electrocardiograms (ECG), Electroencephalogram (EEG) and Electromyogram (EMG).

MATLAB package will be used in the thesis work which is a powerful tool for the

interactive design in most of the scientific applications and complex engineering

calculations.

As an additional in order to achieve the goal of thesis it will also be investigated and

implemented for the removal of harmonics (hum) and high frequency noise from ECG

signal by using general notch rejection filters, which are partial milestone for the thesis.



1 CHAPTER-1

THESIS INTRODUCTION

1.1 Problem Description

The medical monitoring devices are more sensitive for the biomedical signal recording

and need more accurate results for every diagnosis. It is complicated to get accurate

result for every biomedical signal’s recording while patient is diagnosis by medical

monitoring equipments such as ECG, EEG and EMG.

The low frequency signal is destroyed by power line interference of 50/60 Hz noise, this

noise is also source of interference for biomedical signal recording. The signal can also

be corrupted by electromagnetic field (EMF) by the machinery which is placed nearby.

[1] The frequency of power line interference 50/60 Hz is nearly equal to the frequency

of ECG, so this 50/60 Hz noise can destroyed the output of ECG signal while the patient

is diagnosis at hospital or some where else. The recording of ECG signal can not give

accurate result due to the power supply or by environment. [1]

There are many reasons for the corruption of ECG signal while recording in hospital or

some other place due to the external interference which comes from power

transformer or high voltage electric power lines and internal interference comes from

the internal power supplies. Other problem occurs by harmonics and high frequency

noises. In a noise signal, the signal component holds harmonics with different amplitude

and frequency. The harmonics frequency is integral multiple of fundamental frequency

such as 50Hz. Due to these interferences the quality of ECG signal can not be ideal so it

is needed to improve the quality of required output of ECG signal.

1.2 The Purpose of Thesis

The fundamental purpose of this thesis is to remove 50/60 Hz noise and other single

frequency tones from ECG signal by the designing and implementation of least mean

square (LMS) algorithm based upon the FIR filters using MATLAB environment. The

additional milestone of the thesis is to investigation and implementation of the removal

of harmonics and high frequency noise by using general notch rejection filters from ECG

signal in MATLAB environment.



1.3 Report Layout

This section provides a summary of the all the chapters covered in this report.

1.3.1 Chapter-1

This chapter gives the introduction to the thesis, the problem description, purpose and

also detail of report layout of the thesis report.

1.3.2 Chapter-2

This chapter provides the details of problem of power line interference in ECG. And also

present the general overview, heart mechanism & purpose of ECG diagnosis, description

of the thesis, details of the background and motivation, thesis specifications, aim &

objectives of the thesis and this chapter also contain why using MATLAB package.

1.3.3 Chapter-3

This chapter details the basic theory of digital filters, digital signal processing, what are

filters & digital filters, advantages of digital filters, categories of digital filters,

computational property & structure of digital filters algorithm and also contains an

overview on the digital filter’s order, step-size & coefficient.

1.3.4 Chapter-4

This chapter provides the introduction of adaptive filters and its explanation. It also

provides the detail of adaptive filters with respect to digital signal processing, adaptive

filtering concept, general structure for adaptive filtering and performance, stability and

robustness of adaptive algorithm. This chapter also gives the details of convergence

criteria and system identification configuration using an adaptive filter.

1.3.5 Chapter-5

This chapter provides the introduction to adaptive algorithm, advantages of adaptive

filters and adaptive algorithm, FIR filters details, its advantages and disadvantages. It

also gives a brief comparison of the two filters and why the FIR filters and LMS algorithm

is best suited for this thesis. It also gives the brief description of the filtering solution for

removal of power line AC interference and adaptive FIR filter processor.



1.3.6 Chapter-6

This chapter presents the brief description of adaptive filter algorithm and the least

mean square (LMS) algorithm which is to be employed in this thesis to perform the

noise cancellation. It also gives the overview of the structure & operation of the LMS

algorithm, the design of adaptive filter algorithm, noise cancellation adaptive noise

cancelation and interference cancellation.

1.3.7 Chapter-7

In this chapter the design, analysis and simulation results are described. It also give the

details of main objective & how design by DSP technique and the technique of software

implementation & verification for refinement for signal by LMS, which includes removal

of power line interference from ECG signal & removal of power line interference from

voice signal and also described its simulation results. It also gives the detail and graphs

of removing of humming and high frequency noise from ECG signal. Finally the algorithm

implementation and verification has been presented.

1.3.8 Chapter-8

This chapter provided the conclusion and future research. It also gives the detail of the

thesis goal, its achievement and what has been concluded after completion this thesis.

1.3.9 References

The list of information gathered from books, university library database, journals and

internet sites.



2 CHAPTER-2

INTRODUCTION TO ECG SIGNAL WITH POWER LINE INTERFERENCE

2.1 General Overview

The electric power lines are main source of electricity transportation from grid station to

the consumers. Power transformers are used for the transform of voltage which is

generated from the grid station.

The purpose of electricity generation is for the powering electronic & electrical

technologies acquired from various sources of energy. The source of energy for first

power plant was wood, while today it relies mainly on coal, nuclear energy, natural gas,

hydroelectric and petroleum geothermal sources. [2]

Due to the large amount of power involved, transmission normally takes place at high

voltages (110 kV or above). Electricity is usually transmitted over long distance through

overhead power transmission lines. Most transmission lines operate with three-phase

alternating current (AC). The standard frequency in North America is 60 Hz; while 50 Hz

in rest of world.

The power line interference 50/60 Hz is the source of interference in bio potential

measurement and it corrupt the biomedical signal’s recordings such as

Electrocardiogram (ECG), the Electroencephalogram (EEG) and the Electromyography

(EMG) which are extremely important for the diagnosis of patients. It is hard to find out

the problem because the frequency range of ECG signal is nearly same as the frequency

of power line interference.

The figure 2.1 shows the one period of uncorrupted ECG signal with QRS complex. The

ECG signal contains the information within the frequency range of around 50 Hz that is

why it is called QRS complex. The QRS complex is a waveform which is most important

in all ECG’s waveforms and it comes into view in usual and unusual signals in an ECG. [3]



Figure 2.1- ECG signal with QRS complex [3]

Adaptive filters are used to eliminate the power line interference (60 Hz) and they are

proposed to obtain the impulse response of the normal QRS complex. [4] In the figure

above, an uncorrupted ECG signal shows an original signal graph for ECG signal which

demonstrate the diagnosis of heart activities for heart patient.

Consequently, it is analysis that how to remove the power line interference of 50/60 Hz

which is a problem for biomedical signal measurement. Electromagnetic interface (EMI)

from 50/60 Hz power line noise is present in cable holding ECG signal. [5]

Several solutions for the removal of power line interference have been expressed. The

main source of interference is AC power line interference. The interference is caused by

magnetic fields as well as by the electric fields. When special signal recording techniques

are applied, which minimize the interference therefore some AC noise remains as a

consequence of unbalanced input impedances. Further removal of AC noise must be

accomplished either by analog or digital filters.

2.1.1 Heart Mechanism and Purpose of ECG Diagnosis

The heart is a muscular organ, it pump the blood throughout the body and collecting

blood circulating back from the body. [6] Electrical impulses are the main source of

generation of regular normal heartbeat. The heart muscle must be activated electrically

before the beginning of its mechanical function. When the electrical abnormalities of

the heart occur then the heart cannot pump blood properly and supply enough to the



body and brain. This can cause unconsciousness within second and death within

minutes. [7]

An ECG recording is important for clinical diagnosis and treatment; it is a graphical

recording of electrical impulses generated by heart. The ECG is needed to be done when

chest pain occurred such as heart attack, shortness of breath, faster heartbeats,

irregular heartbeats, high blood pressure, high cholesterol, check the heart’s electrical

activity. [6]

2.2 Background and Motivations.

The Electrocardiograph (ECG) signal is an electrical signal generated by the heart’s beats

and can be used to examine some of the functions of the heart. The ECG signal can be

distorted with noise of 50/60 Hz and by some other sources. The noise from electric

power system is a major source of noise during the recording or monitoring of ECG. [8]

Different noises have different frequencies; the noise with low frequency is being

problem with ECG signal and some time high frequency noises also interfere ECG i.e.

mobile phone. If the physical or mathematical variable changes rapidly then it can be

high frequency and if it changes slowly then it would be low frequency. If the variable

does not change at all then it is said that it has zero frequency. The frequency is

measured in cycle/second or in "Hertz". For example the electric power used in daily life

in United State is 60 Hz and 50 Hz in the rest of world.

Most of the electronic devices such as ECG, transmitter, receiver, computer etc get

power from power line. The 50 Hz alternative current (AC) is reduced in voltage,

rectified and than filter to obtain low voltage direct current (DC). This is used to give

power to those electronic devices. [9] Numbers of adaptive filter solution had been

proposed for noise cancellation in ECG. The adaptive filter remove or reduces the mean

squared error between primary input (ECG signal) and the reference input (noise with

ECG signal) [4]

While recording ECG signal, the critical problem is unwanted noise from power line

interference. There are different noises which affect ECG signal but 50/60 Hz

interference from power line distribution is most critical and also 1 Hz power line

interference due to patient’s movement. Various methods were developed for the

removal of power line interference from last two decade. The suitable and prime

methods were based on ECG filtering. [10]

There have been different filtering solutions, which were introduced for the removal of

power line AC interference. The crucial problem of power line interference was found in

ECG signal. In this project the power line interference of 50/60 Hz is major purpose to

remove it from ECG signal. Different filtering solution has been studied to find out the



best solution for the removal of power line interference from ECG signal. Digital filter

has been selected to overcome this problem; there are few filtering solutions which

were examined before to manipulate the power line interference from signal which can

be divided into following categories. [10]

.

• Low Pass Filters

• General Notch-Rejection Filters

• Adaptive Filters

• Global filters

In the thesis two filtering solutions has been chosen for the removal of power line

interference, its respective harmonics and high frequency noise from Original ECG

signal. The removal of power line interference (50Hz) from ECG signal can be removed

by adaptive filtering while the harmonics and high frequency noise can be removed by

implementing general notch rejection filters.

2.3 Thesis Specifications.

The fundamental aim of thesis is to analyze the power line interference by starting a

simple approach from fundamentals of digital signal processing (DSP), digital filters and

then adaptive filters with LMS implementations. The power line interference, some

other signal frequency tones signals and harmonics impacts on the ECG signal which can

be described by MATLAB software simulation.

The main objective is to remove 50 Hz power line interference from ECG signal by using

LMS adaptive algorithm based upon FIR filter. The additional milestone of the project is

to remove harmonics and high frequency noises by using general notch rejection filters

and windowed sinc low pass filters. This method can be employed in a number of useful

applications in which the prime concern is to get the original ECG signal and the

contaminated entities are critically removed.

2.4 Thesis Aims and Objectives.

• To describe the power line interference, main cause of power line interference in

ECG Signal and to carry out a literature survey on removal of power line interference

from ECG signal.

• To give solution for the removal of power line interference in ECG signal and to

investigation of different methods and to point out the best possible methodology

for the removal of power line interference.

• To search for the adaptive filtering technique for removal of 50/60 Hz power line

frequency interference and to have extensive knowledge in, DSP i.e. adaptive

filtering, FIR, IIR, LMS algorithm etc



• To illustrate the suitable method or process to remove the noise, other unwanted

components, undesired tones and interferences from information signal.

• To search for the best possible method available to be used for the removal of

power line interference through the internet, journals & books and analysis of

different kind of signals using MATLAB software.

• In additional to investigate and analyze the harmonics and high frequency

interference in original ECG signal and to remove these noises by using general

notch rejection filters and windowed sinc low pass filter.

• In the project, the deductive experimental research strategy is preferable, in this

view the investigation, observation and testing to get the desired objectives can be

accomplished on the basis of experimental works and to continue the future

research and development regarding this view.

2.5 The Choice for MATLAB Software

MATLAB is commercial software product, which is available from the Mathworks. It

consist of main ‘engine’ having strong mathematical function built-in which perform the

computational and other extended-function libraries for special purpose applications.

[11]

The MATLAB software provides a variety of functions that make it easy and flexible

while simulation for interactive designing, advance analyzing, exploration and visualizing

signals, filters and windows. It provides the tools for finite impulse response (FIR) and

infinite impulse response (IIR), digital filter design, implementation and analysis. It also

provides the toolbox for application such as speech & audio processing, medical imaging

& instruction, wired & wireless communication and financial modeling & analysis. [12]-

[14]

MATLAB has set of construct for plotting scientific graphs from raw or computed data.

[11] It is a high performance language, most productive development and interactive

environment for engineering and technology implementations software package.

MATLAB enables to perform different functions which included, electronic

programming, technical computing applications, scientific & engineering graphical

illustration, accurate numerical calculation, algorithms development, application

development including graphical user interface building, graph and report or software

simulation etc. [12]- [14]



3 CHAPTER-3

BASIC THEORY OF DIGITAL FILTERS

3.1 Digital Signal Processing (DSP)

Digital signal processing (DSP) is well-known as compared to analog signal processing in

different applications. [13] The signals are time varying quantities which carry

information i.e. audio signal, video signals, biological signals (electrical pulses from the

heart) and communications signals. [11] A digital signal is define as the signal that has

discrete amplitude and time. These signals are represented by sequences of numbers

with finite precision and can be used when processing information by computer. [15]

The processing of the signals which deals with sound and images are known as Digital

Signal Processing. In DSP the digital signal processor can be a small microprocessor or a

large programmable digital computer, which perform the desired operations on the

input signal. [16] The application of Signal Processing has grown very fast and

implemented the advanced techniques in speech recognition, image recognition, image

enhancement, audio enhancement, noise reduction, speech & audio encoding and

storage, digital music, communication and data transmission, biometrics, biomedical

applications, radar, sonar and military applications. [13]–[11] Digital signal processing

systems are introduced in many different applications such as multimedia, video

recording, CD player, mobile phones, computers and modem, DSP systems acquired

famous due to their reliability, accuracy, small physical sizes and flexibility.

3.2 What are Filters

A filter is a device when a signal is given; it changes to some desired form by changing its

shape, amplitude, frequency or phase frequency. They are usually employed to remove

the noise, extract information signals and separate two or more combined signals. [17]

There are two main classes of filter, analog and digital filters. These filters are used for

different applications; the selection for the filter depends upon the required output of

the application.



3.3 What are Digital Filters?

Digital filters and signal processing systems or algorithms which are classified as

discrete-time systems and are normally implemented on a digital signal processing (DSP)

chip or special purpose hardware and software in a general purpose computer. These

software approaches are in a mean of computational structures. Analog filters are

replacing by the digital filters because of digital filter’s well known advantages and good

performance in the advanced era of communication system. [18] Digital filters are in

smaller size, much lower component tolerances, greater accuracy, greater reliability,

ability to share multiple filtering tasks than analog filters. [19]

There are two types of filters that can be design as analogue or digital filters. Digital

filters are progressively replacing analogue filter day by day. [20] The designing of the

digital filter needed to remove the unwanted noise from the original signal i.e. if the a

signal x(k) is processed in a discrete system the output signal will be y(k), if this output

signal y(k) is different from the original signal x(k) then it must be needed to modify the

system to get the required output. Then digital filter will be the solution to manipulate

this problem. [19] Digital filters are extremely used in noise cancellation, echo

cancellation and also in the field of biomedical engineering to remove unwanted noise

from ECG, EMG and EEG.

As with the advancement in the technology many signal manipulations like

multiplication, subtraction, differentiation, PID and filtering which were previously

carried out through dedicated hardware are now implemented equally well or even

better by the use of Processors (microprocessors, DSP chips, microcontrollers, CPLDs

etc).Once a signal is captured and converted through ADC, it becomes a numerical value

with certain characteristics, any kind of mathematical algorithm then can be written to

manipulate this value. After the required manipulation the desired output can be

produced using the DAC converter. Digital Filters are same as the analogue filters as far

as their functions is concerned, which is to separate a desired portion of signal

frequencies from the undesired ones but their physical realization is quite different as in

essence digital filters are different mathematical relations written in a specific algorithm

meant to be executed by computers.

3.4 Advantages of Digital Filters

The digital filters can provide many advantages; a brief summery is given below.

1 The charm of the digital filters lies in the fact that digital filters are realized in the

form of piece of software so can be adapted for any required amendment with

out any increase in cost or effort on the electronic circuit.



2 As digital filter is a programmable filter are often implemented in a computer

using a high level programming language so it can be reused if required to

produce cost effective solution. In digital filters for digital design the

characteristics of digital component do not change over time [21]

3 Plenty of support is available for design and testing of digital filters in the form of

CAD and other pre-built package on a general-purpose computer or workstation.

4 By using programmable processes it can be easily modified to change its

frequency response or other characteristic. [17]

5 Realization of the digital filters can be made using the generic hardware (PC,

DAC, ADC, CPLDs) without indulging in the design of specific hardware, which

also helps in reducing the cost and time required in this process.

6 Digital filters can be used in biomedical instruments where frequency is very low

and analog filters are unpractical. [17]

7 Digital filters are most common use in any modern communication system and

digital systems are unaffected by temperature variation. [21]

8 With the advancement in technology the digital filters can be managed at low

frequency signals precisely. The technology of the DSP is increasing very fast, so

the digital filter are applied for the high frequency signal as well i.e. RF (radio

frequency) domain, which in the past was the limited to analog technology. [22]

9 Digital filters can be seen as the direct result of the advancement made in the

computers and computing technology so it will continue to benefit from the

increase in speed and power of computing chips in the future.

10 Digital filters are small in size, consume less power and can be implemented with

less cost and it also store data for future use. [17]

11 Digital filters can made accurate processing, permits the implementation of

many different operations and become more economical. [19]

3.5 Types of Digital Filters

The most imperative tools of DSP are a digital filtering. The separations of signals are

principally utilized by electronic filters, which are combined and the refurbishment of

distorted signals that can be distorted due to the certain reasons. Digital filters are

implemented in real time, the desired output is removal of noise and they are

implemented in dedicated hardware or computer using a high level language. [17] By



the software control, digital filter can be easily changed and are well-suited to do this

task as compared to analogue filters because of their outstanding results.

The digital filters are divided into two basic types, Finite Impulse Response (FIR) and

Infinite Impulse Response (IIR) filters. [23]- [13] - [24] which are known as non recursive

and recursive filters. [25] These types of digital filters can perform paramount required

tasks yet they are categorized either as non recursive filter known as Finite Impulse

Response (FIR) filters or a recursive filter known as Infinite Impulse Response (IIR)

filters.[26]- [25] The term non recursive filter & finite impulse response (FIR) filter and

recursive filter & infinite impulse response (IIR) filter are almost synonymous. [19]. Non

recursive that as implied by the name has a finite length impulse response and recursive

that has an impulse response of infinite length. Both types of filters can be used in the

realization of the noise cancellation but an FIR filter was chosen since it is simple and

stable. [26]

The variety of design methods has been involved for the designing of digital filters to

meet different specifications. The lowest order filter is chosen to avoid the overdesign.

The choice between the filter type (recursive and non recursive) is done due to the

computational property and the storage required for the implementation.

3.6 Computational Properties and structure of Digital Filters Algorithm

The computational property of digital filters algorithm is most important for its

structure. For any digital filter structure it must be needed to work out its

computational property because the computational property of the digital filter

algorithm affect on the performance of digital filter. For the description of

computational properties of digital filter algorithm latency and throughput are used.

Latency is the time for the data flow which applied to a general digital algorithm to

reach the output. Throughput is the measurement of frequency input data applied to a

system. [21]

The structure of digital filter can be described by signal flow graph, they are used to

convert a given transfer function into computational procedure. The structure used is

depending on type of the filter. In IIR filter’s commonly used forms are direct form,

cascade form and parallel form and in FIR filters the direct form or transversal structure

is most widely used because of its ease of implementation. Two other structures are

frequency sampling and fast convolution techniques [17]



3.7 DIGITAL FILTER ORDER, STEP-SIZE AND COEFFICIENTS

The design of digital filter involves determining the order of filter and the values of

coefficients in the representation of different equation. [19] The order, step-size and

coefficient are essential to define performance of a digital filter, which are described

below:

3.7.1 Order of a Digital Filter

The filter order describes the maximum exponents in the numerator or denominator of

z-transform equation of digital filter [28] and also expressed as the number of previous

inputs which are used to calculate the current output. [27] The order of the digital filter

is important for its performance. If the filter order is larger, then better frequency

magnitude response performance of the filter can be achieved.

In FIR filters there is no denominator in its transfer function so it is often equal to the

taps. In IIR filters it is equal to number of delay elements in filter structure. [28]

Different filter’s orders are describes as:

3.7.1.1 Zero-Order Filter

The zero-order filter is described as the current output yn depends only on its current

input xn and not on any previous input. [27]

yn = xn

3.7.1.2 First-Order Filter

The first-order filter only use the previous input and the current input is not used, so the

previous input (xn-1) is required to calculate yn. [27]

yn = xn-1

3.7.1.3 Second-Order Filter

The second-order filter compute the current output yn, two previous inputs (xn-1 and

xn-2) are needed; this is therefore called a second-order filter. [27]

yn = (xn + xn-1 + xn-2) / 3



3.7.2 Step-Size of a Digital Filter

Step-Size is necessary for the use of LMS algorithm, which can be determine by the

cross-correlation between the reference and primary signals.

The step-size depend of the eigen value, if the eigen value is maximum then the step-

size for convergence will also be maximum. The rate of convergence is proportional to

the step-size and the minimum eigen value, which is shown in the following equation:

[26]

1/τ ≈ 2µλmin

In the equation above, µ is the step-size, λmin is the minimum eigen value, and τ is the

overall time-constant.

3.7.3 Coefficient of the Digital Filter.

Coefficient of the digital filter is known as tap weight, which is used to multiply against

delayed signal sample values within a digital filter structure. For an FIR filter, the filter

coefficients are the impulse response of the filter. [28]

The coefficient of the digital filter can be expressed clearly from the equations which are

described in the previous section in ‘’order of digital filter’’ and are shown in following

table. [29]

In the table above the zero-order, first-order and second-order of digital filter is

presented, which shows the coefficient of the digital filter as well. The constants e.g. a0,

a1, a2 ... showing in the above equations are called the filter coefficients.

Zero order:

yn = a0xn

First order:

yn = a0xn + a1xn-1

Second order:

yn = a0xn + a1xn-1 + a2xn-2



4 CHAPTER-4

ADAPTIVE FILTERS

4.1 Introduction

The adaptive filter can be defined as, a filter which self adjust its transfer function

according to an optimizing algorithm and object can be achieve by the modification of

its characteristics. [2] Adaptive signal processing has been introduced and its growth to

the advanced related fields of digital computing, DSP and high speed integrated circuit

technology has been made rapidly. The least mean square (LMS) adaptive filtering

algorithm’s first paper was published in 1959 by Widrow and Hoff. [30]

Adaptive filters are extensively used in the variety of application and they had been

firstly proposed by Kelly of Bell Telephone Laboratories around 1965, [20] most of the

applications are in telecommunication for the cancellation of noise and echoes in the

transmission channel and also used in digital controller for active noise control. [31]

An adaptive filter is a digital filter whose characteristics change in an unknown

environment input signal. In the advanced era of cellular phone, digital television,

wireless communication and digital multimedia commercial services, advanced adaptive

signal processing may give the better solution for the technical problem. [30] The

adaptive filter is also used in the field of biomedical, sonar, radar and image signal

processing, telecommunication for noise cancellation etc.

4.2 Explanation of Adaptive Filter

Adaptive signal processing is more famous due to the property of its digital techniques

which is characterized by flexibility and accuracy in the field of communication and

control. [32] In the advancement of digital signal processing’s application, adaptive filter

become more popular in different devices such as medical monitoring equipments,

mobiles phones and other communication devices. Most of the adaptive filters are

digital due to the complexity of optimizing algorithm, which perform digital signal

processing and adapt their performance based on the input signal. [2] When the fixed

specification of any application is unknown or can not be satisfied by time invariant

filters then an adaptive filter is required to manipulate this problem.



4.3 Adaptive Filters and Digital Signal Processing

The designing of digital filter requires the approved specification with fixed coefficients.

If this specification is time varying or not accessible then this problem can be

manipulate by digital filter with adaptive coefficients, which is know as adaptive filter.

[33] The adaptive fitters are utilized and successfully increased its application under

several regions of telecommunications and biomedical engineering i.e. interference

reduction, noise, speech and image encoding, echo cancellation, equalization of

dispersive channels, and system identification. [34]-[33]

Digital signal processing has well-known repute in the modern times, which is used for

the number of different application in different fields of technologies; biomedical

engineering is one of them where the unwanted noise from ECG can be removed by

digital filters. [34] In the modern era of communication system, adaptive signal

processing is one of the most important technologies used for numbers of different

algorithms. Generally the main problem in the biomedical systems is noise cancellation,

which is considered as adaptive noise cancellation in hi-tech and mature technology

found in the in biomedical systems, telecommunications systems, industrial control,

aerospace, and music etc. [35]

Adaptive filtering is the technique which is used to set the parameters. [33] It is one of

several tools which are made available by the digital signal processing (DSP). Usually

filters are essential part of any system which performs any kind of manipulation or

signal processing to eliminate any unwanted portion or noise induced in the signal.

So the digital filters have an appearance in the form of adaptive filtering, which provides

better performance by adjusting to changes in the noise factors.

4.4 Adaptive Filtering

Adaptive filtering is properly used due to its esteemed knowledge of signal makeup,

that’s why signal analysis is related to the adaptive processing. [32] Literally, the word

’adaptive’ means to adjust with other environment (system) by having the same

response as the system itself to some phenomenon which is taking place in it

surroundings. Or technically the system which tries to adjust its parameter, depending

upon the other system’s behavior and it’s surrounding. The systems which carries out its

functionality after undergoes the process of adaptation is called filter. The term ‘filter’

means to take the unnecessary particles (frequency component) from its input signal

and process them to generate required output under certain specific rules. [36] There

are various principal option for the implementation of adaptive signal processing, e.g.

the LMS algorithm. [31]



The adaptive filters are much famous due to their economical quality, fast processing,

their short period of time adaptation and residual error is small after adaptation. [25]

Adaptive filtering is the most important technique which is used is numbers of

biomedical applications. [4]

The principal of adaptive filter is required to understand the adaptive filtering clearly

which is showed in the figure 4.1. The error signal e(n) can be generated by the output

of the programmable, variable-coefficient digital filter subtracted from a reference

signal y(n). [32]

Fig. 4.1-Principle of an Adaptive Filter [32]

The adaptive filter can be classified in the following areas: [32]

• The optimization criterion

• The algorithm for coefficient updating

• The programmable filter structure

• The type of signal processed

4.5 The General Structure of Adaptive Filters

There are numbers of different structures for the implementation of adaptive filter; the

type for the structure chosen is based on the requirement of the application and

computational complexity of the process. [33] The basic structure of the adaptive filter

is shown in figure 4.1, here the input signal is filtered for the required output and then

PROGRAMMABLR DIGITAL FILTER

ADAPTIVE ALGORITHM

FOR COEFFICIENT UPDATING

+ X(n)

Input Signal

y(n)

y(n)

e(n)

Reference



passed through further processing. The filter’s output is observed by determines its

quality for particular application. After measuring the quality it also examined by a

circuit whether it is need to improve the quality of the output signal. This processing

loop continues until the filter’s parameters are adjusted properly, so the filter’s output

quality should be as good as possible. [37]

2

Figure 4.2- The general structure of an adaptive filter. [37]

The choice of filter structure and adaptation algorithm is important for the design

adaptive filter; the structure can be non recursive or recursive. [25]

4.6 Performance, Stability and Robustness of the Adaptive Algorithm

The performance of the adaptive algorithm is important for all systems; it is also

essential how adaptive system is functioning. For any application the adaptive algorithm

provide competent performance evaluations for the structures of various filter and

adaptive algorithm.

The LMS algorithm is the most popular adaptive algorithm and its performance is

dependent on the filter order, signal condition and convergence parameter (μ). [38] The

adaptive system is used for the solution for any practical problem; the question appears

about the stability of adaptive algorithm whether or not the algorithm is stable. In

general the adaptive filters based on FIR structure are naturally stable. [30]

Adaptive Filter

Filter Adaptation Rules

Quality Assessmen

t

Filter Outpu

t

Filter Input



To satisfy the robustness of the adaptive algorithm the value of step size μ needs to be

small. [39] Robustness is an important criterion which is difficult to measure in a

quantitative approach. The satisfaction for the robustness of the adaptive algorithm can

be gained by the removal of external noise disturbances and arithmetic quantization

noise. [30]

4.7 Convergence Criteria for Adaptive Algorithm

The convergence criterion is the important performance in the adaptive algorithm

which must be according to the required or particular application. [30] For the

convergence of LMS algorithm there are different procedures. The LMS algorithm must

has the convergence condition, which is necessary for the convergence of the mean is

E [є (n)] → 0 as n→ ∞ [1]

The convergence ability of the LMS algorithm can be examined by the range of

convergence factors which provide the stability. [33] Faster convergence is better

solution for the allocation of additional resources in high frequency operation such as

mobile radio, cellular telephone, digital television (HDTV). In low frequency application

such as adaptive echo cancellation and audio band noise cancellation, the convergence

criterion is slow and this simple and adequate solution is provided by LMS algorithm.

[30]

The convergence performance of the LMS algorithm for FIR filter structure is controlled

by the autocorrelation matrix Rx.

[30]

The condition of the satisfaction can be checked and LMS algorithm’s condition must be

satisfied if the step size parameter satisfies the condition. [1] The autocorrelation matrix

Rx is necessary for the convergence. The condition which is important for the

convergence criterion and the convergence factor of LMS algorithm must be chosen in

the range is

0< μ < 1 / λ max [33]-[30]

Were λ max is the largest eigen value of the correlation matrix Rx. The speed of the LMS

algorithm’s convergence is dependent on eign value. [33] The choice of μ in the locality

of 1/ λ max is the best convergence for the adaptive algorithm. [1]-[30]

)]()(*[ nxnxERxT

=



If the matrix Rx has large eigenvalue then the vaule of μ must be much smaller than the

upper band. As a result the convergence speed of the coefficient will be primarily

dependent on the value of the smallest eigenvalue. [33]

4.8 System Identification Configuration Using an Adaptive Filter

When both the unknown system and adaptive filter are prepared by the same input

signal x(n) then adaptive filter is used in system identification configuration.[30] To

reduce the problems of system identification, adaptive filter have excellent ability to

match its output to unknown system and due to adaptive filter’s best capability for

adaptation, it is also used for the removal of interference and disturbance in the signal.

[34] In system identification configuration, the desire signal is the output of unknown

system [33] and the input signal x(n) is set for under analysis, the reference signal a(n) is

produced with input signal and the error signal e(n) is generated by the system output.

[30]-[32]

e(n) = d(n) - y(n)

Figure 4.3- System Identification Configuration for Adaptive Filter [34] -[30]-[32]

The parameters of the adaptive filters are then activated to minimize the particular

function error signal e(n). In system identification configuration when the adaptive filter

accumulated the stable values then error signal e(n) will be reduced.[30] It can be

possible for adaptive filter to converge it to a good model to match after convergence of

Unknown System H(z)

Adaptive Filter

H(z) ^

^ y(n)

a(n)

y(n)

noise, w(n)

input, x(n)

+

+

∑

+

- ,

output

error, e(n)

output d(n)



the unknown system by giving sufficient degree of freedom to the adaptive filter. [34]-

[33]

The system identification configuration is the essential adaptive filtering concept. [30]

This is used to remove the error signal while processing of any input signal with noise. It

is necessary for good performance of adaptive filter to remove the noise which is mixed

with input of the system; otherwise this noise appears at the output and can decrease

the quality of the output.



5 CHAPTER-5

ADAPTIVE ALGORITHM FOR FIR FILTERS

5.1 Introduction

The adaptive algorithm for FIR filters are is widely used in different applications such as

biomedical, communication and control due to its easily implementation, stability and

best performance. Its simplicity makes it attractive for many applications where it is

need to minimize computational requirements.

5.2 Advantages of Filters and Adaptive Algorithm

Today’s medical monitoring equipments and other devices facing variety of interfering

signals which are usually corrupted by noise and other interferences. The power line

interference (50/60 Hz) in ECG signal is the major problem in the field of biomedical

(medical monitoring equipments) and field of communication (cell phone and

communication devices). So filters play an important role for removal of unwanted

signal or noise from original input signal by removing the selected frequencies from

incoming signal. They became much popular due to the increase of the digital signal

processing.

The designing of the adaptive filter, it’s rational to choose the adaptive algorithm and

LMS algorithm can be selected for this designing purpose, which is core contributing

factor for the success of algorithm functioning. [30] Filters are used in biomedical

instruments, as the frequency of biomedical instruments are very low so digital filters

are much popular for low frequency applications. [17]

For any application of the adaptive filters, the input signal and the reference input

required being process; the least mean square is used to adjust the weight of the

adaptive filter in order to minimize the error. The best solution to remove the unwanted

signal or noise from the input signal, the reference noise must be filter out by using

adaptive filtering method due to its good performance and reliability.



5.3 Finite Impulse Response (FIR)

A finite Impulse Response (FIR) filter are type of digital filters [40] and consists of

weighting sequence (impulse response) among non-recursive digital filters which is

finite in length. [41] FIR filters are non recursive digital filters [40] has been selected for

this thesis due to their good characteristics and can be used to implement in any sort of

frequency response digitally. The series of multipliers, delays and adders are used for

FIR filters’ implementation for filter’s output. The output of the non recursive digital

filter is formed from the weighted linear combination of current input and previous

value of the input. [19]

Figure 5.1- Finite impulse response (FIR) filter structure [42]

The filter structure of FIR is presented in the figure 5.2, which described the relationship

between input and output sequences which also described the basic structure and

diagram of FIR filter having a length of N (where N is filter order) and the input samples

are operated by the delays of results. All the delayed samples are multiplied by suitable

coefficient as the hk is the coefficient value for multiplication for output at time n. [42]

The selection of FIR filter is due to coefficient sensitivity, round off noise, stability and

suitable for high speed applications. [13]

FIR and IIR filters are two different classes of digital filters, these digitals filters can be

implemented for different application. The selection of any type of digital filter is based

on the practical implementation of required application. The FIR filter is mostly applied

for adaptive filtering and the main choice of FIR filter was its stability and robustness.

∑ +

+ + +

X X X X

7 -1

7 -1

7 -1

7 -1

y(n) ^

a n a 2 a 1 a 0



5.4 FIR Filters Advantages and Disadvantages

The FIR filter has linear phase characteristics and its operation in for the finite history of

data. FIR is used to manipulate the corrupted data and it operates with less period of

time. Following are the advantages and disadvantages of FIR filters. [24]

5.4.1 Advantages:

� FIR Filter are Linear Phase

� Coefficients are easy and simple to calculate

� The design methods are generally linear

� Complex filters with many band of different gains

� FIR filters are always Stable

� They can be realized efficiently in hardware

5.4.2 Disadvantages:

� Lower Selectivity than IIR filters

� High filter order required for "sharp" frequency edges

5.5 Comparison between FIR and IIR Filters

The non recursive (FIR) and recursive (IIR) filters have different characteristics for

numbers of applications. The non recursive filters are chosen due to its best

performance of numerical operations, differentiation and integration. [25] The table

below shows the comparison between FIR and IIR filters.[43]

IIR FILTERS FIR FILTERS

More Efficient Less Efficient

Analog Equivalent No Analog Equivalent

May Be Unstable Always Stable

Non-Linear Phase Response Linear Phase Response

More Ringing on Glitches Less Ringing on Glitches

CAD Design Packages Available CAD Design Packages Available

No Efficiency Gained by Decimation Decimation Increases Efficiency



Comparison between the different characteristics of FIR and IIR can be made in variety

of ways. The most important benefit of FIR filters over IIR filters is the flexibility in

preferred frequency retort. The FIR filter might be ideal when hardware minimization

and delay minimization are important. [43] Its easy to design the non recursive filters as

compared to recursive filters. [25] Most of the applications for adaptive FIR and IIR

filtering include noise and echo cancellation and the FIR and IIR structures can be used

as adaptive filters and Stability problems. FIR filters are used for all practical

applications. [44] Reliability which is always an important issue regardless of the nature

of the design, is also an advantage offered by the FIR filters over IIR filters.

5.6 Adaptive FIR Signal Processor

There are specific functions for any signal processor to complete its tasks. For this

purpose there must be some type of algorithm to control the process to give correct and

required output for the system. Adaptive FIR signal processor is one of the famous

algorithms to manipulate and minimize the signal error.

In the figure 5.3 adaptive signal processor’s model function is shown, the input signal

x(k) is taken and the output y(k) is showed with the error signal e(k). The adaptive FIR

algorithm is used to manipulate or minimization of the power of the error signal e(k),

this algorithm is called adaptive signal processing algorithms. The error signal must be

minimized by adapting the signal x(k), such that the filter output y(k) is very similar to

some desired signal d(k). [35]

Figure 5.2- The Adaptive Signal Processor [35]



This Adaptive FIR signal processing model can be used for different applications which

are as follow,

(a) Noise cancellation

(b) System identification

(c) Inverse system identification

(d) Prediction



6 CHAPTER-6

LEAST MEAN SQUARE (LMS) ALGORITHM

6.1 Adaptive Filter Algorithms

There are many types of algorithms which had been developed to use in adaptive digital

filters i.e. LMS (Least Mean Square), RLS (Recursive Least Square, NLMS (Normalized

Least Mean Square), etc. The best algorithm to utilize in the removal of power line

interference, most commercial applications favors the LMS. This is mainly because it is

easy to implement and exhibits stability in performance.

6.2 Introduction to LMS Algorithm

The LMS algorithm is extensively used in different application of adaptive filtering due to

low computational complexity, stability and unbiased convergence. [33] In any signal’s

processes there can be error occurred in the required output. There must be suitable

algorithm needed to manipulate this problem. The least mean square (LMS) algorithm is

introduced to minimize the error between a given preferred signal and output of the

linear filter by adjusting recursively the parameters of a linear filter. [45] The more

suitable and basic algorithm for the adaptive filtering is LMS, which is also famous for

the stability of the system. [46] LMS is the most important algorithms in whole family of

algorithms, which has been developed for minimizing the error. [45] This algorithm is

used for the better condition of input signal to attain the faster convergence [33] and

can address a range of problem settings, computational restrictions and minimization

criteria. [45]

Every application needs its simple and easy solution, the LMS algorithm has been

selected for this thesis due to its simplicity, robustness and ease of implementation.

Simplicity and robustness are its major future and it is the widely used in adaptive

filtering algorithm for different applications. [47] The different areas where LMS

algorithm is used include adaptive signal processing, system identification and adaptive

control. [46] Due to its simplicity and robustness, it has made the standard for the

adaptive filtering and is much famous for the different application as compared to other

linear adaptive algorithms. [48]

Least mean square algorithm has lots of benefits in different applications; it has been

productively used in many applications due to the following performance aspects. [45]



� LMS have the ability to reject noisy data due to minute step size parameter μ.

� LMS demonstrate slowly time varying system.

� LMS algorithm does not get stuck at undesired local minima.

� LMS is computationally simple memory competent.

In general LMS adaptive filter removes noise or obtains a desired signal by adapting the

filter coefficient with least-square algorithm based on given filter. [49] The performance

of the LMS algorithm is very high and it is simple in implementation for the removal of

low frequency noise. The suitable value for step size parameter μ can be selected

according to the application’s requirement.

6.3 Overview of the Structure and Operation of the LMS Algorithm

LMS is used for the simplification of gradient vector computation. [33] The overview of

the structure and operation of the LMS algorithm can be discussed according to LMS

algorithm’s properties and its processes. [48] The main property of LMS algorithm is its

convergence behavior in a stationary environment. [33] LMS is a linear adaptive filtering

algorithm and is consists of two basic processes.

� Filtering Process

Filtering process is used to calculate the output of linear filter and to generate an

estimated error by comparing this output with a desire response. [48]

� An Adaptive Process

An adaptive process is used for the automatic adjustment of the filter’s parameters in

accordance with the estimated error. [48]

Figure 6.1- LMS Adaptive Algorithm [50]

LMS adaptive filter L,µ,∆,α

Z -∆

Primary input d + e

y

Reference input

∑

x

-



In the figure 6.1, the overview of least mean square (LMS) algorithm is shown. The

primary input has been taken, where ‘X’ is the reference input. The error signal occurs

for the desired output, there LMS adaptive filter has employed to manipulate the error.

The error signal manipulated by the adaptive algorithm is describe as

e(n) = d(n) - y(n) [50]

The equation above shows the desired signal and the filter output, where d(n) is the

desired signal and y(n) is the filter output. For the minimization of error signal the input

vector x(n) and e(n) are employed. Here it needs to work according to the criterion that

is supposed to minimize. The input vector is used to update the adaptive coefficients

according to that criterion. The criterion used here is the mean-square error (MSE) e:

e = E[e2(n)] [50]

6.4 Design of an Adaptive Filter Algorithm

The adaptive filters are self designing filters, which determine the updating of filter

coefficients requires the extra information in the form of signal. This signal is called

desired or reference signal. [33]

The signal processing system for adaptive filters processes different signal in different

algorithm grounded in statistical basis. [51] The adaptive filters are used for those

applications where it needs to operate for high speed, it is essential to minimize the

hardware complexity. [33] Due to simple mathematics of the LMS algorithm, it focuses

on its transversal filter structure: the input data vector which is stored in the delay

elements of the filter is computed as a linear combination with its output. [51]

The Adaptive algorithm tries to minimize an appropriate objective or error function that

involves the input, reference and filter output signal. This algorithm can be consist of

three parts, the definition of minimizing algorithm, the definition of objective function

and the definition of error signal. [52] The LMS algorithm is much attractive for different

application due to its simplicity and accessible analysis under idealized conditions. [33]



Figure 6.2- Outline of adaptive transversal filter [51]

The outline of adaptive signal processing system is describes in figure 6.2. The input to

the adaptive filter is described as scalar real-valued discrete-time signal x(n) where n is

the time index. At time n, the samples x(n), x(n - 1), . . . through x(n -N + 1) are

simultaneously present in the delay elements of the filter.

6.5 Noise Cancellation

The noise cancellation is severe problem in signals, the process d(n) in noise cancellation

is estimated from a noise corrupted observation.

x(n) = d (n) + v1 (n)

There must be some information about d(n) or v1 (n) for the separation of signal from

noise. The reference signal may be used to estimate the noise v1 (n), and this estimate

may then be subtracted from x(n) to form an estimate of d(n). [47]

Transversal Filter

Adaptation Algorithm

+

y(n|n-1)

c(n-1)

d(n)

+ x(n)

e(n)



Fig 6.3- Noise Cancellation Example [47]



The Fig 6.3 describe the complete process of noise cancellation step by step

(a) Represent the information signal,

(b) Represent the noise signal,

(c) Represent the mixed signal of information and noise signals,

(d) Represent the original signal after filtration.

The principle of noise cancellation is to obtain noise signal and subtract it from the

corrupted signal. The required signal can be found after subtracting the corrupted signal

from noise. [36] The figure above represents the information signal (a) and the noise

signal (b), both the signals are mixed together and then mixed signal (c) is displayed. To

remove the noise signal (b) from information signal (a) there must be some filtration

method which is based on the application requirement. The original signal (d)

represents the output signal after filtration.

6.6 Adaptive Noise Cancellation

Adaptive noise cancellation can be consideration as an outgrowth of the interference

cancellation. One of the adaptive noise cancellation applications was to remove 50/60

Hz noise from ECG signal. [53]

Figure 6.4- Block Diagram of Adaptive Noise Canceller [30]-[31]-[47]-[48]

Adaptive Filter

Signal Source

Noise Source

d(n) Primary

Input e(n)

x(n)

Reference Input

y(n)

+

Filter Output

Error Signal

s + no

n1

z

System Output



At the primary input signal ‘s’ is measured together with noise is assumed to be the sum

of an information signal and sinusoidal interference. For monitoring of the noise ‘n1’ a

reference input supplies a correlated version of the sinusoidal interference. The

correlation of the noises ‘no’ and ‘n1’ is assumed to be high and have same origin so that

influence of the useful signal ‘s’ is negligible at the reference input. [31] The filter uses

the reference input to provide an estimate of sinusoidal interfering signal contained in

the primary input. The adaptive filter forms as estimate of ‘no’ thus by subtracting the

adaptive filter output from the primary input signal. So the information signal with noise

is cancelled at the output by adaptive noise cancellation method. [30]

There are two important characteristics of LMS algorithm i.e. canceller behaves as an

adaptive notch filter, which is tunable and the notch in the frequency response can be

made very sharp by choosing the small value of the step size parameter μ. [48] The

noise cancellation is required to remove unnecessary noise from the given signal. The

term cancellation principle is used to detect the noise and subtract that noise from the

corrupted signal. Its feasibility depends upon the availability of a noise signal originating

signal. The concept of noise cancellation in its simplest form is described in figure 6.3.

6.7 Interference Cancellation by Adaptive Filtering

There are numbers of interferences in different applications in different fields; in the

field of biomedical engineering interference cancellation is severe problem for

biomedical signals such as ECG, EEG and EMG signals. In our case power line

interference 50 Hz is core problem for ECG signal. Adaptive filtering is the best solution

to remove power line interference from biomedical signals.

In figure 6.5 the adaptive filtering for interference cancellation is shown. The unknown

interference can be cancelled or removed by this class of adaptive filtering from primary

signal. The desired output by adaptive filtering is concerned to its primary signal. [54]

Figure 6.5- Interference Cancellation by Adaptive Filtering [54]

Adaptive filter

System Output 1

Reference Signal

Primary Signal

u y +d

e

-∑

(d



According to above adaptive interference cancellation method the reference signal is

employed as an input to the adaptive filter. The sensor (s) which supplying the primary

signal can derive a reference signal in such a manner that the information bearing signal

becomes essentially undetectable or weak. [54]



7 CHAPTER-7

DESIGN, ANALYSIS AND SIMULATIONS

7.1 Main Objective

The goal was to implement and analyze of different noise removal techniques in ECG

signal. Removal of power line interference 50/60 Hz from ECG signal and how to apply

the adaptive LMS algorithm for removing of power line interference and its harmonic

from signals that has been corrupted and the original information contained by

unwanted interferences was main purpose of the thesis. The additional milestone of the

project was to investigation and implementation for the removal of harmonics and high

frequency noise from ECG signal in MATLAB environment.

Numbers of algorithms can be implemented in ECG signal to remove the different type

of noises. In this thesis, two different types for removal of noises have been

implemented.

– Removal of Power Line Interference by Adaptive LMS Algorithm from

original ECG Signal.

– Removal of harmonics and high frequency noise by general notch

rejection filter from original ECG signal.

While the thesis problem and purpose was not as simple to solve and implement as it

might, the possible benefits were enormous. The challenges for the project were the

study of most sensitive biomedical monitoring equipments such as Electrocardiogram

(ECG), electroencephalogram (EEG) and electromyography (EMG). The thesis is basically

research oriented; therefore sufficient reference materials were not available easily. The

results, analysis, implementation and conclusion of the thesis are totally depends upon

better understanding of ECG signal’s simulation and calculation. It was totally out of

domain so a lot of journals, research papers, internet, university library database and

books are read to analyze and understand it in a better way.



7.2 Design by DSP Technique

In digital signal processing (DSP) it is mainly encounter with discrete time signals which

are functions of integers. The signals are also represented by mathematical function like

sinusoidal function or linear difference equations.

In this thesis it deals with two signals i.e. input ECG signal (50 Hz) and noise signal (50

Hz) from power line source. In the case of removal of noise by adaptive LMS algorithm,

this was implemented because of easy to implement and exhibits stability in

performance.

The ECG signal of 50 Hz is taken and mixed with noise signal of 50 Hz; if nothing is

known about noise signal then it can not be subtracted from ECG signal. But in this case

the noise signal of 50 Hz is eliminated by using adaptive LMS algorithm which estimates

the noise related to input noise and subtracts it from input signal to generate the

estimated signal’s output. The LMS algorithm changes the filter coefficients and working

system subtracts it from the actual system’s outputs.

The frequencies among 47 Hz and 53 Hz are more critical for ECG signal of 50 Hz. These

frequencies can be noise for the ECG signal and due to it the quality of ECG recording

can be get down. So nothing seems to be best to use adaptive filter which overcome the

information loss in the ECG recording. For a good DSP system it must fulfils many

requirements, i.e. it must responds to all input frequencies, should be stable, more

reliable for the manipulation of signals.

The most important objective for the choice of adaptive filters was its ability to adjust

the filter’s coefficients and the main designating factor was how to define rules or

algorithms that upgrade coefficients. The adaptive filters judge the performance from

signal and it also tract the signal, develop the solution and determine how filter

coefficients should be upgraded.

7.3 MATLAB Software Implementation

MATLAB is the most useful environment for engineering and technology

implementations software package. It is used for the specific purpose in different fields

of technology based on electronic programming, scientific & engineering graphical

illustration, accurate numerical calculation and algorithms development etc. The

algorithm has been designed and implemented the least mean square (LMS) adaptive

filter based upon the FIR filtering using MATLAB environment. The adaptive filtering is

selected with the objective of removing 50/60 Hz noise from ECG signal. The code is

written for input signal which is supposed to be ECG signal of frequency 50 Hz and the

second signal of noise (frequency1=50 Hz) which is power line interference of 50 Hz has



generated. The FIR adaptive filter has then implemented there and LMS algorithm has

been developed to filter out the low frequency noise from ECG signal. The simulation

results with graphs for ECG signal were then plotted to compare the filtered output by

putting different values of LMS step size and filter tap to visually measure the simulation

program performance. Finally the algorithm implementation and verification has been

presented which increases the reason for the selection of LMS algorithm based on FIR

filters in MATLAB environment. The affects of μ on convergence rate and stability for

the LMS adaptive filter has been examined to achieve the desire results.

The simulation of harmonics of high frequency noise has also been generated to find out

another filtration method in MATLAB environment. The general notch rejection filter

and windowed sinc low pass filter has been developed in MATLAB for the

implementation and removal of harmonics & high frequency noise to achieve the

required output.

7.4 Verification for Refinement of Signal by LMS

The verification for refinement of signal by LSM can be done with the removal of power

line interference (50 Hz) from ECG signal.

7.4.1 Removal of Power Line Interference (50 Hz) from ECG Signal by LMS Algorithm

The ECG signal has been taken and LMS adaptive filter algorithm has been developed.

The ECG signal of 50 Hz is displayed in MATLAB environment as ECG Signal and than the

noise of 50 Hz is generated and then mixed with the ECG Signal, which is displayed as

Mixed signal. The adaptive filter is implemented by using LMS algorithm, FIR filter has

been designed. The ECG Signal, 50 Hz Noise signal, Mixed signal, Error signal and

Adaptive LMS filtered output signal have been displayed. The output is nearly same as

the ECG inputted signal.



7.4.1.1 Simulation for Power Line Interference and its Removal from ECG Signal

FilterTap=16;

mu = 0.005;

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0

1Original ECG Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0

150 Hz Noise Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0

2Mixed Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-5

0

5Error Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0

2LMS Filtered Output

ECG Signal Simulation-1



FilterTap=16;

mu = 0.009;

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0


0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0

150 Hz Noise Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0

2Mixed Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-5

0

5Error Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0





FilterTap=32;

mu = 0.005;

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0


0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0

150 Hz Noise Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0

2Mixed Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-5

0

5Error Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0





FilterTap=32;

mu = 0.009;

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0


0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

0

150 Hz Noise Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0

2Mixed Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-5

0

5Error Signal

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-2

0



In the figure ECG Signal Simulation-1, the value of the filter tap and µ has been taken 16

and 0.005 respectively to generate the graph. The figure shows different plots, first,

second, third, fourth and fifth plots are taken as to be ECG signal, 50 Hz noise signal,

mixed signal, error signal and filtered output signal respectively. The ECG signal of 50 Hz

and noise signal of 50 Hz (which is supposed to be power line interference) are

generated and then mixed together in third plot of the figure. The fourth pot of the

figure shows the error signal which has been calculated by the difference of original ECG

and 50 Hz noise signal. The fifth plot shows the LMS filtered output of the mixed signal

which is nearly same to the input ECG signal. It is noticed that the system shows

adaptation after subtracting the noise of 50 Hz from ECG signal.



In the second figure ECG Signal Simulation-2, the value of filter tap and µ are taken as 16

and 0.009, which shows different results as compared to the ECG Signal Simulation-1. It

is concluded that the rate of convergence is changed by changing the value of µ.

In the figure ECG Signal Simulation-3, the value of filter tab has been changed from 16 to

32 and µ is taken as 0.005. This shows the ECG signal (50 Hz) and noise signals (50 Hz)

are mixed together and the filtered out by using LMS adaptive filter. This figure can be

compare with the ECG Signal Simulation-4 where the value of filter tab and µ are taken

as 32 and 0.009 respectively. In this simulation graph the value of µ is decreased which

shows the small change in the coefficient and the convergence of filter act as slowly. So

it is concluded that with large step-size the filter convergence takes place fast. It is also

concluded that with the large value of µ, the filter convergence act as fast. By changing

the results and convergence rates, finally it is concluded that the LMS adaptation take

place properly and it performed adaptation.

7.4.2 Removing of Harmonics and High Frequency Noise from Original ECG Signal

To the verification of removal of noise from original ECG signal, another method has

been developed for the implementation and analysis of different noise removal

technique in ECG signal. The test for the simulation of ECG signal has been taken by

adding different noises.

Humming which is also known as low frequency noise has been taken and added in the

original ECG signal. The major work is concerned with removing undesired frequency

harmonics while saving the original information in the signal as much as possible during

this elimination process.

Biomedical signals play an important role for monitoring of patient’s ECG. High

frequency noise can also be added with ECG signal while diagnosis of patient in hospital

or some where else. This high frequency noise can be added due to the use of Mobile

phone near patient or some other sources.

The original ECG signal with noises is passed through notch and windowed sinc low pass

filter, which filter out hum and high frequency noise portion from the ECG signal. With

this process the unwanted noise signal can be removed from ECG signal, and then

original ECG signal without noise can be obtained.

The graph of original ECG signal with hum (low frequency noise) and high frequency

noise is displayed in figure below. In the first plot of the figure the original ECG signal

has displayed and the hum and high frequency noise are displayed in second and third

plots respectively. Then both noises humming and high frequency noise has been added

to the original ECG signal, which is shown in the fourth plot as mixed signal.



Notch rejection filter is employed for the removal of humming (50 Hz). As there are two

different noises in this case i.e. humming and high frequency noise, both noises after

passing through the notch filter, the signal with high frequency noise remain with the

original ECG signal in the fifth plot of the figure.

Finally the corrupted signal is passed through windowed sinc low pass filter to retrieve

the original ECG signal. The high frequency noise is then filtered out by using windowed

sinc low pass filter and the desire output of the ECG signal has then achieved at the final

output. By comparing the graph of input original ECG signal with the output, it is

concluded that the overall result of method and technique developed in this thesis is

achieved. The goal for the noise cancellation or removal of different noise frequencies

has been performed satisfactory.

7.4.2.1 Simulation for Harmonics and High Frequency Noise and its Removal from

Original ECG Signal

0 200 400 600 800 1000 1200-1

0

1

EC

G

0 200 400 600 800 1000 1200-1

0

1

HU

M

0 200 400 600 800 1000 1200-20

0

20

HF

-No

ise

0 200 400 600 800 1000 1200-20

0

20

Mix

ed

Sig

0 200 400 600 800 1000 1200-20

0

20

Wit

ho

ut

Hu

m

0 200 400 600 800 1000 1200-2

0

2

Ou

tpu

t

Original ECG Signal with HUM and High Frequency Noise Simulation by Notch Filter



After analysing the filtering technique for humming and high frequency noise from ECG

signal, it is concluded that implementation and analysis has been performed more or

less the same and it also shows the method and filtering technique developed for the

removal of harmonics and high frequency noise from ECG signal performed its operation

and meet the required results.

7.5 Algorithm Implementation and Verification

Biomedical signals play a critical role in the diagnosis of patients. ECG is a medical

monitoring device which is used for the diagnosis of heart patient. As power line

interference 50/60 Hz is major problem in ECG signal. An algorithm for the LMS adaptive

filter was suggested, as the ECG signal can be variously mixed with power line

interference of 50 Hz. The LMS adaptive filter is widely used to filter the ECG signal as its

convergence causes good performance. To verify the performance of the LMS adaptive

algorithm, ECG signal has been selected and evaluated the performance of the proposed

filtering technique.

The MATLAB environment was used for the simulation of ECG signal. The code contents

of the source file used in this thesis were collected from various sources. For the

completion of code, the collected contents were modified according to the application’s

requirement and placed in the required sequence. To design the FIR filter, these source

files were used to configure the DSP technique. After designing of FIR filter the LMS

algorithm has been executed and verified.

Two basic processes are involved when the LMS algorithm is applied, a filter process

involving the computation of the output of FIR filter produced by a vector of tap inputs

and an estimation error signal calculated by comparing this output to a desired

response.

LMS algorithm is extensively used in different application of adaptive filtering due to its

computational simplicity and FIR filter is also popular because of its simplicity and

inherent stability. An important parameter is the step size μ, it affects the convergence

rate and stability of the LMS adaptive filter. If μ is small, it will create a slower rate of

convergence but is more accurate and stable. On the other hand, if it is large, it will

converge faster but will become less accurate and less stable.

Moreover another method has been implemented for the removing of harmonics

(known as low frequency noise) and high frequency noise from original ECG signal. The

humming and high frequency noise has been removed by using general notch rejection

filters and windowed sinc low pass filter. The original ECG signal (50 Hz) has been taken

and mixed with the hum and then both the ECG and Hum signals are added with high



frequency noise of 375 Hz. After passing the ECG signal with both noises through notch

filter, the ECG signal with high frequency noise remains. Then this remaining signal with

high frequency noise has been passed through the windowed sinc low pass filter to get

rid of high frequency noise. By use this method the original ECG signal can be retrieved.

By investigating this method, it is concluded that the overall result of the technique is

achieved. The main goal for the removal of different noise i.e. harmonics and a high

frequency noise has been performed satisfactory.



8 CHAPTER-8

8.1 CONCLUSION AND FUTURE RESEARCH

8.1.1 Conclusion

This report is devoted to the problems and solutions on removal of Power Line

Interference and other Single Frequency Tones from Signals. The understanding of noise

cancellation from ECG signal was explained clearly to the readers, the methods and

techniques applicable to be used discussed through out the report. It has been

proposed a solution for the power line interference its respective harmonics and high

frequency noise interferences from original ECG signal. The results have been obtained

which were required in purpose statement of the report.

In general FIR filters are used because these types of filters have simple architecture and

are logically stable, so the FIR filter was chosen for the development of the system. The

research has been made for the selection of filters and algorithm, two kind of adaptive

filters i.e. FIR (Finite impulse response) & IIR (Infinite impulse response) and two kinds

of algorithms, the LMS (least mean square) & RLS (recursive least squares) algorithms

were studied and examined. The LMS algorithm is the most widely used adaptive

filtering algorithm in biomedical monitoring equipments, so it was decided to be

employed for the thesis to get the required solution for the main purpose. The

applications of the LMS algorithm can be implemented due to its simplicity and

robustness.

An adaptive filter is used in applications that require different filter characteristics in

response to variable signal conditions. The speed of adaptation and accuracy of the

noise cancellation after adaptation are important measures of performance for noise

cancellation algorithm. The goal of the adaptive filter is to match the filter coefficients

to the noise so that the adaptive filter can subtract the noise out from signal. So

adaptive filtering technique was selected to achieve the goal of thesis.

The test for the simulation of ECG signal has been taken. The signal is corrupted by

power line interference of 50 Hz. It is observed that the frequency of the power line

interference is 50 Hz which is then mixed with original ECG signal, it is also examined

that the mixed signal is displayed on the plot. After passing through LMS algorithm the

filtered output is nearly same as the input signal with some acceptable distortion range.

The value of step size μ play an important role in determining the convergence speed,

stability and residual error after convergence. The convergence rate was controlled by



LMS step size μ. The ECG signal graphs described in the simulation results verify the

adaptation of the LMS adaptive algorithm by changing various parameters like step size,

convergence value (µ) and filter taps have various effects on the output graphs. The

result shows that LMS is an effective algorithm used for the adaptive filter in the noise

cancellation implementation.

By increasing the filter order it shows a convergence rate but makes the results more

precise and by decreasing the step size value it creates the slower convergence but

improves the stability and accuracy. The recovered signal closely resembles to the

original simulated signal minus the noise. It can be seen that the implementation of the

algorithm functions as correctly and efficiently. By comparing the graphs of the input

signal of ECG and output signal, it is noticed that the simulation program performs

satisfactorily and that noise cancellation from original ECG signal is acquired. The overall

performance of LMS algorithm for power line interference is achieved.

Furthermore the general notch rejection filters method also performs the correct

operation while filtering the noise from original ECG signal. This technique for the

investigation, implemented and analysis of removal of harmonics and high frequency

noise from original ECG signal performed satisfactory. It is concluded that the low

frequency noise (hum) and high frequency noise can be removed from original ECG

signal by the implementation of general notch rejection filters method and the desired

result can be achieved accurately.

8.1.2 Suggestion for Future Work/Future Enhancement

The depth knowledge achieved is in a number of aspects by using digital signal

processing techniques with MATLAB package for medical monitoring equipments (ECG).

It provides the real concepts along with the theoretical backgrounds of removal of

power line interference, single frequency tones and high frequency noise from original

ECG signal. This enhances the understanding and self confidence in the field of

electronics and biomedical engineering.

In the thesis, the adaptive signal processing filtering technique based on LMS algorithm

could be implemented for more signals and also improvement of the thesis can be

further implemented with different algorithms such as NLMS and RLS to achieve the

desired results. It could also be investigate and implement the removal of multiple of

harmonics from ECG signal.

In further research it would be of interest to make a broader study and look at some

companies for related project for the implementation.



9 APPENDIX A

9.1 MATLAB CODE FOR ECG SIGNAL

% Removal of Power Line Interference from ECG Signal

% 50 Hz Noise removal from ECG signal by the implementation of LMS algorithm

clear;

clc

close all;

fullscreen = get(0,'ScreenSize');

figure('Position',[ fullscreen(3)/4 fullscreen(4)/4 fullscreen(3)/1.5 fullscreen(4)/1.5])

% Create the signal

% Original ECG signal

Fs = 1000;

Length=1000*10;

i=1:Length;

ECG_signal=ecg(50);

ECG=ECG_signal;

for i=1:Length/50-1

ECG_signal=[ ECG_signal ECG];

clc

end



frequency1=50; % Frequency of Noise Signal

% Range of the ECG Signal

i=1:length(ECG_signal);

Noise_signal = sin(2*pi*frequency1*i/Fs); % Power Line Interference

% Range of the Noise Signal embedded in the ECG

Mixed_signal = ECG_signal + Noise_signal; % ECG Signal Plus Noise

%%%%%%%%%%%%%%%% POWER LINE INTERFERENCE %%%%%%%%%%%%%%%

%%%%%%%%%%%%%Adaptive filtering using LMS algorithm%%%%%%%%%%%%%

%Power line Hum=noise;

x=ECG_signal;

n=Noise_signal;

m=Mixed_signal;

d=x+n+m;

n1=rand()*Noise_signal;

length_filter=15;

w=ones(1,length_filter);

mu=0.005; % Lest Mean Square (LMS) step size.

FilterTap=16;

for i=1:Length

y1=0;

if i<length_filter

for j=1:i

y1=y1 + w(i,j)*n1(i-j+1);

end

else



for j=1:length_filter

y1=y1+ w(i,j)*n1(i-j+1);

end

end

y(i)=y1;

e(i)=d(i)-y(i);

if i<length_filter

for k=1:i

w(i+1,k)=w(i,k) + mu*n1(i-k+1)*e(i); % mu*n1(i)*e(i) ; %

end

else

for k=1:length_filter

w(i+1,k)=w(i,k) + mu*n1(i-k+1)*e(i);

end

end

end

Output_without_Noise_signal=e;

M=100;

fc=0.25;

for i=1:M

h(i)=sin(2*pi*fc*(i-M/2))*(0.42- 0.5*cos(2*pi*i/M) + 0.08*cos(4*pi/M) )/(i-M/2);

end

h(ceil(M/2))=2*pi*fc;

h=h/sum(h);

Final_filter_Output=filter(h,1,Output_without_Noise_signal);

% Display ECG Signal, Noise, ECG Plus Noise and Adaptive LMS Output Signals

% Input is the ECG Signal of frequency 50 Hz

figure(1)



% Original ECG Signal

subplot(5,1,1); plot(x) ;title('Original ECG Signal');

% Power Line Interference (Low Frequency Noise)

subplot(5,1,2);plot(n) ;title('50 Hz Noise Signal');

% Mixed ECG Signal with Power Line Interference (50 Hz)

subplot(5,1,3);plot(m) ;title('Mixed Signal');

subplot(5,1,4);plot(d-e) ;title('Error Signal');

% Filtered Output

subplot(5,1,5);plot(Final_filter_Output) ;title('LMS Filtered Output');

grid on;

hold on;



10 APPENDIX C

10.1 MATLAB CODE FOR HARMONICS AND HIGH FREQUENCY NOISES

FROM ECG SIGNAL BY GENERAL NOTCH REJECTION FILTER

% Removal of HUM and High Frequency Noise from Original ECG Signal by Notch Filter

clear;

clc

close all;

fullscreen = get(0,'ScreenSize');

figure('Position',[ fullscreen(3)/4 fullscreen(4)/4 fullscreen(3)/1.5 fullscreen(4)/1.5])

% Create the signal

% Original ECG signal

Fs = 800;

ECG_signal=ecg(50);

ECG=ECG_signal;

for i=1:20

ECG_signal=[ ECG_signal ECG];

clc

end

scrsz=get(0,'ScreenSize');

maxWindow=[1 31 scrsz(3) scrsz(4)-104];

frequency1=50; % Frequency of Power Line Interference

frequency2=375; % High Frequency Noise

% Range of the ECG Signal



i=1:length(ECG_signal);

HUM = sin(2*pi*frequency1*i/Fs); % Low Frequency HUM Signal

% Range of the Noise Signal Embedded in the ECG

High_Frequency_Noise = 5*sin(2*pi*frequency2*i/Fs + pi/4) +

10*cos(2*pi*(frequency2+50)*i/Fs + 2*pi/7 ) ; % High Frequency Noise Signal

Mixed_Signal = ECG_signal + High_Frequency_Noise + HUM; % ECG Signal Plus Noise

Fn = Fs/2; % Nyquist Frequency [Hz]

W0 = 50; % Notch Frequency [Hz]

w0 = W0*pi/Fn; % Notch frequency Normalized

BandWidth = 10; % -3dB BandWidth [Hz]

B = BandWidth*pi/Fn; % Normalized Bandwidth

k1 = -cos(w0); k2 = (1 - tan(B/2))/(1 + tan(B/2));

b = [1+k2 2*k1*(1+k2) 1+k2];

a = [2 2*k1*(1+k2) 2*k2];

Output_without_Hum=filter(b,a,Mixed_Signal);

M=100;

fc=0.25;

for i=1:M

h(i)=sin(2*pi*fc*(i-M/2))*(0.42- 0.5*cos(2*pi*i/M) + 0.08*cos(4*pi/M) )/(i-M/2);

end

h(ceil(M/2))=2*pi*fc;

h=h/sum(h);



Final_filter_Output=filter(h,1,Output_without_Hum);

figure(1)

% Original ECG Signal

subplot(6,1,1);

plot(ECG_signal)

ylabel ('ECG')

% Low frequency Noise (HUM )

subplot(6,1,2);

plot(HUM)

ylabel ('HUM')

% High Frequency Noise

subplot(6,1,3);

plot(High_Frequency_Noise)

ylabel ('HF-Noise')

% Mixed ECG Signal with HUM and High Frequency Noise

subplot(6,1,4);

plot(Mixed_Signal)

ylabel ('Mixed Sig')

% Output Without HUM

subplot(6,1,5);

plot(Output_without_Hum)

ylabel ('Without Hum')

% Filtered Output



subplot(6,1,6);

plot(Final_filter_Output)

ylabel ('Output')

%grid on;

hold on;



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