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7/27/2019 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
INTRODUCTION
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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).
INTRODUCTIONSignals and Systems:
1 0
( ) 0 0
for n
n for n
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Basic discrete signal representation Unit Step Signal
INTRODUCTIONSignals and Systems:
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)
INTRODUCTIONSignals and Systems:
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
INTRODUCTIONSignals and Systems:
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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.
INTRODUCTIONSignals and Systems:
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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]).
INTRODUCTIONSignals and Systems:
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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.
INTRODUCTIONSignals and Systems:
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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.
INTRODUCTIONSignals and Systems:
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Classification of discrete time system:-
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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Classification of discrete time system:-
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.
INTRODUCTIONSignals and Systems:
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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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Determine whether the system is Causal/non-causal.
a)Let n=2
INTRODUCTIONExample 1 (Causal/non-causal system)
PresentOutput
Presentinput
Passinput
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Determine whether the system is Causal/non-causal.
b)Let n=2
INTRODUCTIONExample 1 (Causal/non-causal system)
PresentOutput
Passinput
But, let n=-2
PresentOutput
Futureinput
Therefore, the system isnon causal J
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Classification of discrete time system:-
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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Classification of discrete time system:-
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.
INTRODUCTIONSignals and Systems:
( ) ( 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)
INTRODUCTIONExample 3 (Recursive/Non-recursive system)
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c)
LHS,
So,
INTRODUCTIONExample 3 (Recursive/Non-recursive system)
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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.
INTRODUCTIONAnalog and Digital Signals Processing:
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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.
INTRODUCTIONAnalog and Digital Signals Processing:
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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
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