introduction to dsp’s - florida institute of technologymy.fit.edu/~vkepuska/ece3551/lecture...

Microcomputer Systems 1

Introduction to

DSP’S

12 December 2014 Veton Këpuska 2

Introduction to DSP’s

Definition: DSP – Digital Signal Processing/Processor

It refers to:

Theoretical signal processing by digital means (subject of ECE3222, ECE3541),

Specialized hardware (processor) that can process signals in real-time (subject of this course ECE3551&3)

This class’s focus is on: Hardware Architecture of a real-world DSP platform

Software Development on DSPs, and

Applied Signal Processing theory and practice.



DSP’s process signals

Signal – a detectable physical quantity or impulse (as a voltage, current, or magnetic field strength) by which messages or information can be transmitted (Webster Dictionary)



Signal Characteristics: Signals are Physical Quantities: Signals are Measurable Signals are Analog Signals Contain Information.

Examples: Temperature [oC] Pressure [Newtons/m2] or [Pa] Mass [kg] Speed [m/s] Acceleration [m/s2] Torque [Newton*m] Voltage [Volts] Current [Amps] Power [Watts]

In this class, analog signals are electrical. Sensors: are devices that convert other physical quantities (temperature,

pressure, etc.) to electrical signals.

Signal and Systems

Introduction to

Signals and

Systems


Introduction to Signals and Systems

Introduction to Signals and Systems as related to Engineering

Modeling of physical signals by mathematical functions

Modeling physical systems by mathematical equations

Solving mathematical equations when excited by the input functions/signals.


Modeling

Engineers model two distinct physical phenomena:

1. Signals are modeled by mathematical functions.

2. Physical systems are modeled by mathematical equations.

What are Signals?


Signals

Signals, x(t), are typically real

functions of one independent variable that typically represents time; t.

Time t can assume all real values: -∞ < t < ∞,

Function x(t) is typically a real

function.


Example of Signals: Speech


Example of Signals EKG:


http://upload.wikimedia.org/wikipedia/en/b/bd/12leadECG.jpg

Example of Signals: EEC


http://upload.wikimedia.org/wikipedia/commons/2/26/Spike-waves.png

Categories of Signals

Signals can be:

1. Continuous, or

2. Discrete:

T – sampling rate

f – sampling frequency – 1/T

– radial sampling frequency – 2f= 2/T


Signal Processing

Signals are often corrupted by noise.

s(t) = x(t)+n(t)

Want to ‘filter’ the

measured signal s(t) to

remove undesired noise

effects n(t).

Need to retrieve x(t).

Signal Processing


Deterministic signal

Corrupting, stochastic

noise signal

What is a System?



Modeling Examples

Human Speech Production is driven by air (input signal) and produces sound/speech (output signal)

Voltage (signal) of a RLC circuit

Music (signal) produced by a musical instrument

Radio (system) converts radio frequency (input signal) to sound (output signal)


Speech Production

Human vocal tract as a system:

Driven by air (as input signal)

Produces Sound/Speech (as output signal)

It is modeled by Vocal tract transfer function:

Wave equations,

Sound propagation in a uniform acoustic tube

Representing the vocal tract with simple acoustic tubes

Representing the vocal tract with multiple uniform tubes


Anatomical Structures for Speech Production


Uniform Tube Model

cos,

cos

sin,

cos

j t

g

j t

g

l x cu x t U e

l c

l x ccp x t j U e

A l c

Volume velocity, denoted as u(x,t), is defined as the

rate of flow of air particles perpendicularly through a specified area.

Pressure, denoted as p(x,t), and

tj

g eUtu )(),0(


RLC Circuit

v(t)

L R

C

i(t)

Voltage, v(t) input signal Current, i(t) output signal Inductance, L (parameter of the system) Resistance, R (parameter of the system) Capacitance, C (parameter of the system)

t

tvdiC

tRidt

tdiL )()(

1)(

)(


Newton’s Second Law in Physics

The above equation is the model of a physical system that relates an object’s motion: x(t), object’s mass: M with a force f(t) applied to it: f(t), and x(t) are models of physical signals.

The equation is the model of the physical system.

2

2 )()(

dt

txdMtf

What is a System?

A system can be a collection of interconnected components:

Physical Devices and/or

Processors

We typically think of a system as having terminals for access to the system:

Inputs and

Outputs


Example:

Single Input/Single Output (SISO) System

Multiple Input/Multiple Output (MIMO) System


Vin Vout

Electrical Network

+

-

+

-

x1 (t)

System

…

x2 (t)

xp (t)

y1 (t)

…

y2 (t)

yp (t)

Example:

Alternate Block Diagram Representation of a Multiple Input/Multiple Output (MIMO) System


System x(t) y(t)

1

2

1

pp tx

tx

tx

t

x

1

2

1

qq ty

ty

ty

ty

System Modeling


Physical System

Mathematical Model

Model Analysis

Model Simulation

Design Procedure

Model Types

1. Input-Output Description

Frequency-Domain Representations:

Transfer Function - Typically used on ideal Linear-Time-Invariant Systems

Fourier Transform Representation

Time-Domain Representations

Differential/Difference Equations

Convolution Models

2. State-Space Description

Time-Domain Representation


Model Types

1. Continuous Models

2. Discrete Models




Analog Continuous

DSP process digital signals:

Analog-to-Digital Converter (ADC)

Binary representation of the analog signal

Digital-to-Analog Converter (DAC)

Digital representation of the signal is converted to continuous analog signal.


ADC

x(t)

Analog

Low-pass

Filter

Sample

and

Hold

fs

b) Amplitude Quantized Signal

xa(nT)

x[n]

Quantizer

DSP

c) Amplitude & Time Quantized – Digital Signal

a) Continuous Signal


Example of ADC


DAC

DSP Digital to

Analog

Converter

Analog

Low-pass

Filter y[n]

y(t)

ya(nT)

c) Continuous Low-pass filtered Signal b) Analog Signal a) Digital Output Signal


Why Processing Signals?

Extraction of Information Amplitude Phase Frequency Spectral Content

Transform the Signal

FDMA (Frequency Division Multiple Access)

TDMA (Time Division Multiple Access)

CDMA (Code Division Multiple Access)

Compress Data ADPCM (Adaptive Differential

Pulse Code Modulation) CELP (Code Excited Linear

Prediction) MPEG (Moving Picture Experts

Group) HDTV (High Definition TV)

Generate Feedback Control Signal Robotics (ASIMOV) Vehicle Manufacturing Process Control

Extraction of Signal in

Noise Filtering Autocorrelation Convolution

Store Signals in Digital

Format for Analysis FFT …


Digital Telephone Communication System Example:


Typical Architecture of a DSP System

Sensor

ADC

Analog Signal Conditioning

Digital Signal Conditioning

DSP DAC

Analog Signal Processing

Digital Signal Processing


Why Using DSP?

Low-pass Filtering example:

Chebyshev Analog Filter of Type I and Order 6, vs.

FIR 129-Tap Filter


Chebyshev Analog Filter of Type I

Chebyshev Type I (Pass-Band Ripple)

6-Pole

1.0 dB Pass-Band Ripple

Non-liner Phase

MATLAB: fdatool Order = 6

Fs = 10,000 Hz

Fpass = 1,000 Hz

Apass = 1 [dB]


Example of a 3-rd order Active low-pass filter implementation


Magnitude Response of Chebyshev Filter Type I Order 6.


Pass-Band Ripple 1.0 dB


Digital Filter Design

FIR,

129-Tap,

Less then 0.002 dB Pass Band Ripple

Linear Phase


FIR Filter Magnitude Response


Less then 0.002 dB Pass-Band Ripple


Analog vs. Digital Implementations

Analog

Cons: Approximate Filter

Coefficients

Only standard components available

Environment Temperature dependent

Less accurate

Can be used only for designed purpose

Pros: Operate in real-time

Digital (DSP)

Cons: Real-time operation is

dependent on the speed of processor and the complexity of problem at hand.

Pros: Accurate Filter

implementation to desired precision

Operation independent on the environment.

Flexible

DSP’s can be reprogrammed.


DSP Implementation of the FIR Filter

129-tap digital filter requires 129 multiply-accumulates (MAC)

Operation must be completed within sampling interval (1/Fs) to maintain real-time. Fs=10000Hz = 10kHz ⇒ 100 s

ADSP-21xx family performs MAC process in single instruction cycle

Instruction rate > 129/100 s = 1.3 MIPS

ADSP-218x 16-bit fixed point series: 75 MIPS.

introduction to dsp’s - florida institute of technologymy.fit.edu/~vkepuska/ece3551/lecture...

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