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ECE 6640Digital Communications

Dr. Bradley J. BazuinAssistant Professor

Department of Electrical and Computer EngineeringCollege of Engineering and Applied Sciences

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Course/Lecture Overview

• Syllabus• Personal Intro.• Textbook/Materials Used• Additional Reading• ID and Acknowledgment of Policies

• Textbook• Chapter 1

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Syllabus

• Everything useful for this class can be found on Dr. Bazuin’s web site!– http://homepages.wmich.edu/~bazuinb/

• The class web site is at– http://homepages.wmich.edu/~bazuinb/ECE6640/ECE6640_Sp17.html

• The syllabus …– http://homepages.wmich.edu/~bazuinb/ECE6640/Syl_6640.pdf

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Who am I?

• Dr. Bradley J. Bazuin– Born and raised in Grand Rapids Michigan– Undergraduate BS in Engineering and Applied Sciences, Extensive

Electrical Engineering from Yale University in 1980– Graduate MS and PhD in Electrical Engineering from

Stanford University in 1982 and 1989, respectively.– Industrial Experience – Digital, ASIC, System Engineering

• Part-time ARGOSystems, Inc. 1981-1989• Full-time ARGOSystems, Inc. 1989-1991• Full-time Radix Technologies 1991-2000

– Academic Experience – Electrical and Computer Engineering• Term-appointed Faculty, WMU ECE Dept. 2000-2001• Tenure track Assistant Professor, WMU ECE Dept. 2001-2007• Tenured Associate Professor, WMU ECE Dept. 2007- present

Research Activities and Interests

• Sunseeker Solar Team Adviser & WMU Educational Solar Garden Technical Director– Embedded processing systems (TI MSP430 based)– Embedded software (control, monitoring, safety, telemetry)– Energy conversion (solar cells, batteries, super capacitors)

• CAPE & CASSS– Center for the Advancement of Printed Electronics– Center for Advanced Smart Sensors and Structures

• Wireless Communications – Physical Layer signal and system implementation– Software Defined Radios (SDR) - USRP & GNU radio– Xilinx with VHDL coding and Graphic processing units (GPU)

• Advanced Digital Signal Processing– Algorithmic techniques for processing detecting, estimating and exploiting signals

(communications, electronics, and sensors).– Multirate signal processing, estimation theory, adaptive signal processing

• Collaborative Engineering– Supporting other WMU research activities where I can contribute

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Required Textbook/Materials

• Bernard Sklar, Digital Communications, Fundamentals and Applications, Prentice Hall PTR, Second Edition, 2001. ISBN: 0-13-084788-7.

• SystemView by ELANIX CD with textbook– We will follow the examples, but use MATLAB

• MATLAB, Student Edition• MATLAB Signal Processing Toolbox

– The MATH Works,MATLAB and Signal Processing Toolbox http://www.mathworks.com/

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Supplemental Books and Materials

• John G. Proakis and Masoud Salehi, “Digital Communications, 5thed.,” McGraw Hill, Fifth Edition, 2008. ISBN: 978-0-07-295716-7.

• John G. Proakis and Masoud Salehi, “Communication Systems Engineering, 2nd ed.”, Prentice Hall, 2002. ISBN: 0-13-061793-8.

• A. Bruce Carlson, P.B. Crilly, “Communication Systems, 5th ed.”, McGraw-Hill, 2010. ISBN: 978-0-07-338040-7.

• Leon W. Couch II, “Digital and Analog Communication Systems, 7th ed.”, Prentice Hall, 2007. ISBN: 0-13-142492-0.

• Stephen G. Wilson, “Digital Modulation and Coding, ” Prentice-Hall, 1996. ISBN: 0-13-210071-1.

• Ezio Biglieri, D. Divsalar, P.J. McLane, M.K. Simon, “Introduction to Trellis-Coded Modulation with Applications”, Macmillan, 1991. ISBN: 0-02-309965-8.

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Identification and Acknowledgement

• Identification for Grade Posting, Course and University Policies, and Acknowledgement

• Please read, provide unique identification, sign and date, and return to Dr. Bazuin.

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Course/Text Overview1. Signals and Spectra.

Digital Communication Signal Processing. Classification of Signals. Spectral Density. Autocorrelation. Random Signals. Signal Transmission through Linear Systems. Bandwidth of Digital Data.

2. Formatting and Baseband Modulation.

Baseband Systems. Formatting Textual Data (Character Coding). Messages, Characters, and Symbols. Formatting Analog Information. Sources of Corruption. Pulse Code Modulation. Uniform and Nonuniform Quantization. Baseband Modulation. Correlative Coding.

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Course/Text Overview (2)3. Baseband Demodulation/Detection.

Signals and Noise. Detection of Binary Signals in Gaussian Noise. Intersymbol Interference. Equalization.

4. Bandpass Modulation and Demodulation/Detection.

Why Modulate? Digital Bandpass Modulation Techniques. Detection of Signals in Gaussian Noise. Coherent Detection. Noncoherent Detection. Complex Envelope. Error Performance for Binary Systems. M-ary Signaling and Performance. Symbol Error Performance for M-ary Systems (M>>2).

Exam #1

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Course/Text Overview (3)5. Communications Link Analysis.

What the System Link Budget Tells the System Engineer. The Channel. Received Signal Power and Noise Power. Link Budget Analysis. Noise Figure, Noise Temperature, and System Temperature. Sample Link Analysis. Satellite Repeaters. System Trade-Offs.

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Course/Text Overview (4)6. Channel Coding: Part 1.

Waveform Coding. Types of Error Control. Structured Sequences. Linear Block Codes. Error-Detecting and Correcting Capability. Usefulness of the Standard Array. Cyclic Codes. Well-Known Block Codes.

7. Channel Coding: Part 2.

Convolutional Encoding. Convolutional Encoder Representation. Formulation of the Convolutional Decoding Problem. Properties of Convolutional Codes. Other Convolutional Decoding Algorithms.

Exam #2

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Course/Text Overview (5)8. Channel Coding: Part 3.

Reed-Solomon Codes. Interleaving and Concatenated Codes. Coding and Interleaving Applied to the Compact Disc Digital Audio System. Turbo Codes.

Appendix 8A. The Sum of Log-Likelihood Ratios.

9. Modulation and Coding Trade-Offs.

Goals of the Communications System Designer. Error Probability Plane. Nyquist Minimum Bandwidth. Shannon-Hartley Capacity Theorem. Bandwidth Efficiency Plane. Modulation and Coding Trade-Offs. Defining, Designing, and Evaluating Systems. Bandwidth-Efficient Modulations. Modulation and Coding for Bandlimited Channels. Trellis-Coded Modulation.

Final Exam

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Course/Text Overview (6)Advanced Topics (as time permits)

11. Multiplexing and Multiple Access.

Allocation of the Communications Resource. Multiple Access Communications System and Architecture. Access Algorithms. Multiple Access Techniques Employed with INTELSAT. Multiple Access Techniques for Local Area Networks.

12. Spread-Spectrum Techniques.

Spread-Spectrum Overview. Pseudonoise Sequences. Direct-Sequence Spread-Spectrum Systems. Frequency Hopping Systems. Synchronization. Jamming Considerations. Commercial Applications. Cellular Systems.

Final Exam

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Text AppendicesA. A Review of Fourier Techniques.

Signals, Spectra, and Linear Systems. Fourier Techniques for Linear System Analysis. Fourier Transform Properties. Useful Functions. Convolution. Tables of Fourier Transforms and Operations.

B. Fundamentals of Statistical Decision Theory.

Bayes' Theorem. Decision Theory. Signal Detection Example.

C. Response of a Correlator To White Noise.

D. Often-Used Identities.

E. s-Domain, z-Domain and Digital Filtering.

F. List of Symbols.

G. SystemView by ELANIX Guide to the CD.

Comments from Previous Offering

• A strong focus on themes and critical results for each chapter covered is desirable. The text author provides his own list of critical elements, they can be incorporated into the instructors set.

• Matlab simulations of all significant concepts should be available. They allow the students to perform theoretical computations and then observe what the computations mean, particularly as it relates to bit-error rate performance, digital modulation and coherent and non-coherent demodulation, and channel encoding and decoding.

• The software that comes with the text provides demonstrations, but it is not user friendly and the software is very out-of-data (no longer supported).

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Chapter 1

1. Signals and Spectra.1.1 Digital Communication Signal Processing.1.2 Classification of Signals. 1.3 Spectral Density. 1.4 Autocorrelation. 1.5 Random Signals. 1.6 Signal Transmission through Linear Systems. 1.7 Bandwidth of Digital Data.

A review of prerequisite material that is critically important when studying digital communication systems.

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Sklar’s Communications System

Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,

Prentice Hall PTR, Second Edition, 2001.

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Simplified Communications System• Format: making the message compatible with digital processing• Source Coding: efficient descriptions of information sources• Channel Coding: signal transformation enabling improved reception

performance after expected channel impairments• Modulation: formation of the baseband waveform• RF Mixing: frequency domain translation of baseband signal• Transmit/Receive: RF Amplifiers and Filters

Information Message Format

Source Encode

Mod-ulation RF Mixing Transmitter

Reformat Source DecodeDemod-ulation RF Mixing Receiver

Antenna

AntennaInformation Message

RF Signal

Noise

Interference

Channel Encode

Channel Decode

Bits Symbols Signals

ECE 6640 20

Communication Channel

• The channel greatly effects received RF signals– Frequencey, Bandwidth, Transmitted Signal Power, RF Propagation– Attenuation, Nonlinear Distortion, Multipath, Range, Direction– Signal-to-Noise Ratio (SNR) and Signal-to-Interference Ratio (SIR)– Minimum Detectable Signal Level (MDS), Noise Floor

TransmittingAntenna

ReceivingAntenna

RF Communication Channel

Noise

Interference

Linear Filtering

NonlinearDistortion

Atten-uation

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Received Signal

• The receiver must extract the original message as best possible!

• Multiple signals with similar channel characteristics may be present

• The RF channel(s) must be allocated and efficiently utilized. – Frequency band assignments and regulations (power, direction, etc.)– Signal modulation structures have different characteristics

tnthtsthtsthtstr NNc 22

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Why Digital?1. Noise, Interference, Path Loss, and Channel Impairments

(signal environment)2. Cost3. Inherent Availability4. Reliability and Reconfigurability



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Terminology



• Information Source• Textual Message• Character• Binary Digit (Bit)• Bit Stream• Symbol• Digital Waveform• Data Rate

Signal Processing Functions

ECE 6640 24Notes and figures are based on or taken from materials in the course textbook:

Bernard Sklar, Digital Communications, Fundamentals and Applications, Prentice Hall PTR, Second Edition, 2001.

Classification of Signals

• Deterministic and Random

• Periodic and Non-periodic

• Analog and Discrete/Digital

• Energy and Power Signals

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SKLAR DSP Tutorial

• The CD that comes with the text includes a “Concise DSP Tutorial” in pdf format

• Table of Contents:– Frequency Domain Analysis – critical importance– General Digital Filters – important– Finite Impulse Response (FIR) Filters – critical importance– Infinite Impulse Response (IIR) Filters – useful but …– Filter Design Techniques – will be discussed and provided– Adaptive Filters – saved for Dr. Bazuin’s ECE6565 course

• Also see Appendix B: Fundamentals of Statistical Decision Theory– Specific material from probability and statistics is required.

(ECE 3800 or ECE5820 material)ECE 6640 26

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Spectral Density

• Energy Spectral Density

• Power Spectral Density

dttxE 2X

2

T

2T

2

0X

0

0

dttxT1P

*X fXfXf

*TTTX

fXfXT1limfG

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Autocorrelation

• of an Energy Signal

dttxtxR XX

• Properties:1. Energy

2. Symmetry

3. Maximum

4. Transform Pair

220 XXERXX

XXXX RR

0XXXX RR

fR XXXX

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Autocorrelation

• of a Power Signal

• Properties:1. Energy

2. Symmetry

3. Maximum

4. Transform Pair

2

T

2T

2

0XX

0

0

dttxT10

XXXX

0XXXX

fGXXXX

2T

2T

TXXdttxtx

T1lim

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Random Signals

1 Distribution Functions Probability Distribution Function (PDF) or Cumulative Distribution Function (CDF) [preferred]

xforxFX ,10 0XF and 1XF XF is non-decreasing as x increases 1221Pr xFxFxXx XX

For discrete events For continuous events

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Random Signals

2. Density Functions Probability Density Function (pdf)

xforxf X ,0

1

dxxf X

duufFx

XX

dxxfxXx

x

xX

2

1

21Pr

Functions of random variables

dydxxfyf XY

Probability Mass Function (pmf)

xforxf X ,0

1

dxxf X

duufFx

XX

dxxfxXx

x

xX

2

1

21Pr

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Random Signals

Mean Values and Moments 1st, general, nth Moments

dxxfxXEX X or

x

xXxXEX Pr

dxxfXgXgE X or

x

xXXgXgE Pr

dxxfxXEX Xnnn or

x

nnn xXxXEX Pr

Central Moments

dxxfXxXXEXX Xnnn

x

nnnxXXxXXEXX Pr

Variance and Standard Deviation

dxxfXxXXEXX X2222

x

xXXxXXEXX Pr2222

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Random Signals

The Gaussian Random Variable

xforXxxf X ,2exp

21

2

2

where X is the mean and is the variance

dvXvxFx

vX

2

2

2exp

21

Unit Normal

duuxx

u

2

exp21 2

xx 1

XxxFX or

XxxFX 1

The Q-function is the complement of the normal function, : (Appendix B)

duuxQxu

2

exp21 2

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Random Processes

5. Random Processes 5.1. Introduction

Ensemble

5.2. Continuous and Discrete Random Processes

5.3. Deterministic and Nondeterministic Random Processes

5.4. Stationary and Nonstationary Random Processes

5.5. Ergodic and Nonergodic Random Processes A Process for Determining Stationarity and Ergodicity

a) Find the mean and the 2nd moment based on the probability b) Find the time sample mean and time sample 2nd moment based on time

averaging. c) If the means or 2nd moments are functions of time … non-stationary d) If the time average mean and moments are not equal to the probabilistic mean

and moments or if it is not stationary, then it is non ergodic.

From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9

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Random Processes: Continuous, Discrete and Mixed

Continuous and Discrete Random Processes A continuous random process is one in which the random variables, such as ntXtXtX ,, 21 , can assume any value within the specified range of possible values. A more precise definition for a continuous random process also requires that the cumulative distribution function be continuous. A discrete random process is one in which the random variables, such as ntXtXtX ,, 21 , can assume any certain values (though possibly an infinite number of values). A more precise definition for a discrete random process also requires that the cumulative distribution function consist of numerous discontinuities or steps. Alternately, the probability density function is better defined as a probability mass function … the pdf is composed of delta functions. A mixed random process consists of both continuous and discrete components. The probability distribution function consists of both continuous regions and steps. The pdf has both continuous regions and delta functions.


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Random Processes: Deterministic and Nondeterministic

Deterministic and Nondeterministic Random Processes A nondeterministic random process is one where future values of the ensemble cannot be predicted from previously observed values. A deterministic random process is one where one or more observed samples allow all future values of the sample function to be predicted (or pre-determined). For these processes, a single random variable may exist for the entire ensemble. Once it is determined (one or more measurements) the sample function is known for all t.


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Random Processes: Stationary and Nonstationary (1)

Stationary and Nonstationary Random Processes The probability density function for random variables in time as been discussed, but what is the dependence of the density function on the value of time, t, when it is taken? If all marginal and joint density functions of a process do not depend upon the choice of the time origin, the process is said to be stationary (that is it doesn’t change with time). All the mean values and moments are constants and not functions of time! For nonstationary processes, the probability density functions change based on the time origin or in time. For these processes, the mean values and moments are functions of time. In general, we always attempt to deal with stationary processes … or approximate stationary by assuming that the process probability distribution, means and moments do not change significantly during the period of interest.


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Random Processes: Stationary and Nonstationary (2)

Stationary and Nonstationary Random Processes The requirement that all marginal and joint density functions be independent of the choice of time origin is frequently more stringent (tighter) than is necessary for system analysis. A more relaxed requirement is called stationary in the wide sense: where the mean value of any random variable is independent of the choice of time, t, and that the correlation of two random variables depends only upon the time difference between them. That is

XXtXE and XXRXXttXXEtXtXE 00 1221 for 12 tt

You will typically deal with Wide-Sense Stationary Signals.


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Random Processes: Ergodicity

Ergodic and Nonergodic Random Processes Ergodicity deals with the problem of determining the statistics of an ensemble based on measurements from a sample function of the ensemble. For ergodic processes, all the statistics can be determined from a single function of the process. This may also be stated based on the time averages. For an ergodic process, the time averages (expected values) equal the ensemble averages (expected values). That is to say,

T

T

nT

nn dttXT

dxxfxX21lim

Note that ergodicity cannot exist unless the process is stationary!


ECE 6640 40

Random ProcessesThe power spectral density is the Fourier Transform of the autocorrelation:

diwtXtXERwS XXXX exp

For an ergodic process,

txtxdttxtx

T

T

TT

XX 21lim

diwdttxtx

TtXtXE

T

TT

XX exp21lim

dtdtiwtxiwttxT

T

TT

XX

expexp21lim

dtwXiwttxT

T

TT

XX

exp

21lim

dttwitxT

wXT

TT

XX

exp

21lim

2wXwXwXXX From: George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,Oxford University Press Inc., 1999. ISBN: 0-19-512354-9

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Binary Sequence, Low Bit Rate



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Binary Autocorrelation and PSD



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Bandwidth Consideration

• The first spectral null occurs are 1/T. Therefore one measure of bandwidth could be the null.

• Are there others bandwidth measures? – 3dB bandwidth– 99% Power– If it were a rectangle with Gx(0) given, how wide would it be

(Noise Equivalent Bandwidth)– Etc.



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Bandwidth Consideration



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White Noise

Noise is inherently defined as a random process.

You may be familiar with “thermal” noise, based on the energy of an atom and the mean-free path that it can travel.

As a random process, whenever “white noise” is measured, the values are uncorrelated with each other, not matter how close together the samples are taken in time.

Further, we envision “white noise” as containing all spectral content, with no explicit peaks or valleys in the power spectral density.

As a result, we define “White Noise” as

tSRXX 0 0SwS XX

This is an approximation or simplification because the area of the power spectral density is infinite!


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Band Limited White Noise

Thermal noise at the input of a receiver is defined in terms of kT, Boltzmann’s constant times absolute temperature, in terms of Watts/Hz. Thus there is kT Watts of noise power in every Hz of bandwidth.

For communications, this is equivalent to –174 dBm/Hz or –144 dBW/Hz.

For typical applications, we are interested in Band-Limited White Noise where

fW

WfSwS XX 0

0

The equivalent noise power is then:

002 20 SWdwSRXEW

WXX

For communications, we use kTB.

How much noise power, in dBm, would I say that there is in a 1 MHz bandwidth?

dBmBdBkTdBkTBdB 11460174

ECE 6640 47

White Noise in Comm.

• From the text



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Noise as A Gaussian Random Process

• What is so special about a Gaussian Distribution?– Result of summing a large number of random variables– Linear systems produce Gaussian Outputs– Well know/studied characteristics– Used to define the characteristics of numerous natural, real-world signals

A Gaussian Random Variable

xforXxxf X ,2exp

21

2

2

where X is the mean and is the variance

dvXvxFx

vX

2

2

2exp

21

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Linear Systems

Linear transformation of signals:

txthty sXsHsY

Convolution Integrals

0

dhtxty

or

t

dxthty

where for physical realizability and stability constraints we require

00 tforth

dtth

ECE 6640 50

Transfer Function

• For linear systems: A sinusoidal input results in sinusoidal output modified in magnitude and phase.

fjexpfHfH

fHRefHImtanf 1

tf2cosAtx 0

txthty

000 ftf2cosfHAty

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Filtering a Random Process

• The PSD of a filtered response is

0222

0111 dhtxdhtxERYY

021212

01 XXYY RhhddR

021212

01 exp diwRhhddRwS XXYYYY

wHwHwSRwS XXYYYY

2wHwSRwS XXYYYY

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Distortionless Transmission and the Ideal Filter

• To receive a signal without distortion, only changes in the magnitude and/or a time delay is allowed.

0ttxKty

0tf2expfXKfY

• The transfer function is

0tf2expKfH

• A constant gain with a linear phase KfH 0tf2f

ECE 6640 53

Ideal Filter (1)

• For no distortion, the ideal filter should have the following properties:

fjexpfHfH

u

u

fffor,0

fffor,1fH

u

u0

fffor,arbitrary

fffor,tf2f

• The impulse response is

u

u

u

u

f

f0

f

f0

dfttf2jexpth

dftf2jexptf2jexp1th

ECE 6640 54

Ideal Filter (2)

0uu

0

0u

0

0u

0

0u

f

f0

0

f

f0

ttf2sincf2thtt2

ttf2sin2th

tt2jttf2jexp

tt2jttf2jexpth

tt2jttf2jexpth

dfttf2jexpth

u

u

u

u

• Continuing

• The sinc function– A non-causal filter



ECE 6640 55

Ideal Filters in the Freq. Domain



ECE 6640 56

Realizable Filters, RC Network



1st order Butterworth

Filter

ECE 6640 57

White Noise in an RC Filter



• The noise PSD has been modified • The autocorrelation is spread in time

ECE 6640 58

Signal Filtering in the Real World



ECE 6640 59

Signal Filtering in the Real World (2)



ECE 6640 60

Bandwidth Considerations, Easy



ECE 6640 61

Bandwidth Considerations, Harder

• If the spectrum extends to infinity, where do you assume that it can be cut off?



ECE 6640 62

Bandwidth Considerations

• Note 1: that as soon as time is limited, the signal has been multiplied by a rect function in the time domain.– A rect in the time domain creates an infinite sinc convolution in the

frequency domain!

• Note 2: that a bandlimited frequency domain signal can be generated by multiplying by a rect function in the frequency domain.– A rect in the frequency domain results in a non-causal, infinite

time convolution in the time domain!

• For mathematicians, a real signal can not be both time limited and frequency band limited?!

ECE 6640 63

Bandwidths that are Used



ECE 6640 64

Bandwidth Definitions

(a) Half-power bandwidth. This is the interval between frequencies at which Gx(f ) has dropped to half-power, or 3 dB below the peak value.

(b) Equivalent rectangular or noise equivalent bandwidth. The noise equivalent bandwidth was originally conceived to permit rapid computation of output noise power from an amplifier with a wideband noise input; the concept can similarly be applied to a signal bandwidth. The noise equivalent bandwidth WN of a signal is defined by the relationship WN = Px/Gx(fc), where Px is the total signal power over all frequencies and Gx(fc) is the value of Gx(f ) at the band center (assumed to be the maximum value over all frequencies).

(c) Null-to-null bandwidth. The most popular measure of bandwidth for digital communications is the width of the main spectral lobe, where most of the signal power is contained. This criterion lacks complete generality since some modulation formats lack well-defined lobes.

ECE 6640 65

Bandwidth Definitions (2)

(d) Fractional power containment bandwidth. This bandwidth criterion has been adopted by the Federal Communications Commission (FCC Rules and Regulations Section 2.202) and states that the occupied bandwidth is the band that leaves exactly 0.5% of the signal power above the upper band limit and exactly 0.5% of the signal power below the lower band limit. Thus 99% of the signal power is inside the occupied band.

(e) Bounded power spectral density. A popular method of specifying bandwidth is to state that everywhere outside the specified band, Gx(f ) must have fallen at least to a certain stated level below that found at the band center. Typical attenuation levels might be 35 or 50 dB.

(f) Absolute bandwidth. This is the interval between frequencies, outside of which the spectrum is zero. This is a useful abstraction. However, for all realizable waveforms, the absolute bandwidth is infinite.

Spectrum and Time Domain of a Band-limited Bandpass Signal

ECE 6640 66Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,


Summary

• Communication must consider a number of aspects– Time and Frequency Domain Signals– Discrete and Continuous Time Signal Constructs– Deterministic and Random Signal Properties– Models of Signal Propagation

• Simple time and amplitude changes• Complex channel impairments

– Models of Other Signals in the Environment• Noise (white, Gaussian, or more complex)• Interference• Multipath

• To successfully model and analyze modern communication systems, there is a lot of prerequisite knowledge required.

ECE 6640 67

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