JEL4233 - 1 Introduction to DSP

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INTRODUCTION

Dr Zakaria Hussain

JEL4233DIGITAL SIGNALS PROCESSING


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Definition of Signal: Any physical quantity (Voltage, current

or velocity)that varies with time (t) or

independent variables and carriesinformation. S1(t) = 5t S2(x,y) = 3x +2xy + 10y

2

Signals may be classified into twocategories depending on the characteristicsof the time-variable they can take:

Continuous Time Signal Discrete Time Signal

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Signals and Systems:


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INTRODUCTIONSignals and Systems:

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Basic discrete signal representation Unit Sample sequence (Unit Impulse).


1 0

( ) 0 0

for n

n for n

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Basic discrete signal representation Unit Step Signal


1 0

( ) 0 0

for n

u n for n

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Basic discrete signal representation Unit Ramp Signal

Complex-valued exponential signal(complex sinusoidal sequence, complexphasor)


2 .

( ) , ( ) 1, arg ( ) 2 .j nT

S

f nx n e x n x n nT f nT

f

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Definition of System: A combination of a few component that

are physically connected to perform a

specific task. Also defined as a physicaldevice that perform operation on a signal.

Systems may also be classified into twocategories:

Continuous Time System Discrete Time System


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Continuous Time System: A system in which continuous time input

signals are transformed into continuous

time output signals.

Discrete Time System: A system that transforms discrete- time

inputs signals into discrete time output

signals.


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Discrete Time System (other definition): A discrete-time system is a device or

algorithm that operates on a discrete time

input signal or excitation (e.g. x[n]),according to some rule (e.g. H[.]) toproduce discrete time output signal orresponse (e.g. y[n]).


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Classification of discrete time system:

Static versus dynamics system

A system is said to be Static(memoryless) if the output at anyinstant (n) depend only (at most) oninput at the same time but not past orfuture sample of input.

A system is said to be Dynamic (withmemory) if the output depends onpresent, past or future input.


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Classification of discrete time system:-

Time invariant versus time variant systems

A system is said to be Time invariant ifits input-output characteristics do notchange with time.

A system is said to be Time variant if

its input-output characteristics changewith time.


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Linear versus non-linear systems

A linear system is one that satisfiesthe superposition principle.

A nonlinear system is one does notsatisfy the superposition principle.


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Causal versus non-causal system (causality)

A system is said to be Causal if theoutput of the system at any timedepends only on present and pastinputs.

A system is said to be Noncausal if thesystem not only depends on present andpast inputs but also future input.


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Determine whether the system is Causal/non-causal.

a)

b)

c)

INTRODUCTIONExample 1 (Causal/non-causal system)

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a)Let n=2


PresentOutput

Presentinput

Passinput

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b)Let n=2


PresentOutput

Passinput

But, let n=-2

PresentOutput

Futureinput

Therefore, the system isnon causal J

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Stable versus unstable systems

A system is said to be bounded input -bounded output (BIBO) stable if everybounded input produces the bounded(finite) output i.e.

An Unstable system usually exhibitextreme behavior and cause overflow inany practical implementation and


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Determine the stability of the system.

Solution:

INTRODUCTIONExample 2 (Stable/Unstable system)

Therefore, the system is stable since JEL4233

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Determine the stability of the system.

Solution:

INTRODUCTIONExample 2 (Stable/Unstable system)

Therefore, the system is unstable since JEL4233

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Recursive versus non-recursive systems

A system whose output y(n) at time ndepends on any number of the pastoutputs values (e.g. y(n-1),y(n-2), )is called a recursive system.

In contrast, if y(n) at time n dependsonly on the present and past input thensuch a system is called non-recursive.


( ) ( 1), ( 2), , ( ), ( ), ( 1), , ( )y n F y n y n y n N x n x n x n M

( ) ( ), ( 1), , ( )y n F x n x n x n M

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Determine whether the system is recursive ornon-recursive.

a)

b)

c)

INTRODUCTIONExample 3 (Recursive/Non-recursive system)

0

( ) ( ) ( )N

k

y n h k x n k

0 1

( ) ( ) ( ) ( ) ( )N N

k k

y n b k x n k a k y n k

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Solution:

c)


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c)

LHS,

So,


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Analog signal processing (ASP) is a signalprocessing that are conducted on analogsignals by analog means.

Examples of ASP include crossover filters inloudspeakers, frequency analyzer and bass,treble and volumecontrols on stereos.

Purpose of ASP includes changing the signal

characteristics or extracting desiredinformation.

INTRODUCTIONAnalog and Digital Signals Processing:

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Digital signal processing (DSP) is a signalprocessing that are conducted on digitalsignals by digital means.

DSP usually used in audio and speech signalprocessing, sonar and radar signal processing,sensor array processing, digital imageprocessing, signal processing for communication

control system, biomedical signal processingetc.


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INTRODUCTION

Example DSPAPPLICATION

MILITARYSecure Communications

Sonar Processing

Image Processing

Radar Processing

Navigation, Guidance

VOICE/SPEECHSpeech RecognitionSpeech Processing/Vocoding

Speech Enhancement

Text-to-Speech

Voice Mail

INSTRUMENTATIONSpectrum Analyzers

Seismic Processors

Digital Oscilloscopes

Mass Spectrometers

MEDICALPatient Monitoring

Ultrasound Equipment

Diagnostic Tools

Fetal Monitors

Life Support Systems

Image Enhancement

INDUSTRIAL/CONTROLRobotics

Numeric Control

Power Line Monitors

Motor/Servo Control

CONSUMERRadar Detectors

Power Tools

Digital Audio / TV

Music Synthesizers

Toys / Games

Answering Machines

Digital Speakers

PRO-AUDIOAV Editing

Digital Mixers

Home Theater

Pro Audio

COMMUNICATIONSEcho Cancellation

Digital PBXs

Line Repeaters

Modems

Global Positioning

Sound/Modem/Fax Cards

Cellular Phones

Speaker Phones

Video Conferencing

ATMs

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The goal of DSP is usually to measure, filterand/or compress continuous real-world analogsignals.

The continuous realworld analog signal isusually been converted to digital signal, bymean of sampling and quantization using ADC,which turns the analog signal into a stream of

numbers before processing digitally. However, often, the required output signal is

another analog output signal, which requires aDAC.


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INTRODUCTIONStereo

AmplifierRecord Player

Tape Deck

Radio

Sound

CardA/D

D

S

P

Sound

CardD/A

Cool Edit

Waveform Editor

Pentium Computer

Analog/Continuous-TimeSignals

Digital/Discrete-TimeSignals

Multichannel (Stereo) Signals

Digital Signal Processing:1) Noise Reduction

-Digital Filtering, etc.2) Signal Compression

-MP3, JPEG/MPEG Image, etc.

3) Spectral Analysis (e.g., FFT)

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Thank You

JEL4233 - 1 Introduction to DSP

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