dsp based projects
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EXPERT SYSTEMS AND SOLUTIONS
Email: [email protected]@yahoo.com
Cell: 9952749533www.researchprojects.infoPAIYANOOR, OMR, CHENNAI
Call For Research Projects Finalyear students of B.E in EEE, ECE, EI,M.E (Power Systems), M.E (Applied
Electronics), M.E (Power Electronics)Ph.D Electrical and Electronics.
Students can assemble their hardware in our
Research labs. Experts will be guiding the projects .
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DIGITAL SIGNAL PROCESSING(DSP)FUNDAMENTALS
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WHAT IS DSP?
Converting a continuously changing waveform(analog) into a series of discrete levels (digital)
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WHAT IS DSP?
The analog waveform is sliced into equalsegments and the waveform amplitude ismeasured in the middle of each segment
The collection of measurements make up thedigital representation of the waveform
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WHAT IS DSP?
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DSP IS EVERYWHERESound applications
Compression, enhancement , special effects, synthesis, recognition,echo cancellation,Cell Phones, MP3 Players, Movies, Dictation, Text-to-speech,
CommunicationModulation, coding, detection, equalization, echo cancellation,Cell Phones, dial-up modem, DSL modem, Satellite Receiver,
AutomotiveABS, GPS, Active Noise Cancellation, Cruise Control, Parking,
MedicalMagnetic Resonance, Tomography, Electrocardiogram,
Military
Radar, Sonar, Space photographs, remote sensing,Image and Video ApplicationsDVD, JPEG, Movie special effects, video conferencing,
MechanicalMotor control, process control, oil and mineral prospecting,
http://www.eas.asu.edu/~dsp/grad/anand/java/Audio/Audio.htmlhttp://www.eas.asu.edu/~dsp/grad/anand/java/Audio/Audio.html -
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SIGNAL PROCESSINGHumans are the most advanced signal processors
speech and pattern recognition, speech synthesis,We encounter many types of signals in variousapplications
Electrical signals: voltage, current, magnetic and electricfields,Mechanical signals: velocity, force, displacement,Acoustic signals: sound, vibration,Other signals: pressure, temperature,
Most real-world signals are analog They are continuous in time and amplitudeConvert to voltage or currents using sensors and transducers
Analog circuits process these signals usingResistors, Capacitors, Inductors, Amplifiers,Analog signal processing examples
Audio processing in FM radiosVideo processing in traditional TV sets
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LIMITATIONS OF ANALOG SIGNALPROCESSING
Accuracy limitations due toComponent tolerancesUndesired nonlinearities
Limited repeatability due to TolerancesChanges in environmental conditions
TemperatureVibration
Sensitivity to electrical noiseLimited dynamic range for voltage and currents
Inflexibility to changesDifficulty of implementing certain operations
Nonlinear operations Time-varying operations
Difficulty of storing information
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DIGITAL SIGNAL PROCESSINGRepresent signals by a sequence of numbers
Sampling or analog-to-digital conversions
Perform processing on these numbers with a digital processorDigital signal processingReconstruct analog signal from processed numbers
Reconstruction or digital-to-analog conversion
A/D DSP D/Aanalogsignal
analogsignal
digitalsignal
digitalsignal
Analog input analog output Digital recording of music
Analog input digital output Touch tone phone dialing
Digital input analog output Text to speech
Digital input digital output Compression of a file on computer
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PROS AND CONS OF DIGITALSIGNAL PROCESSING
ProsAccuracy can be controlled by choosing word lengthRepeatableSensitivity to electrical noise is minimalDynamic range can be controlled using floating pointnumbersFlexibility can be achieved with software implementationsNon-linear and time-varying operations are easier toimplementDigital storage is cheapDigital information can be encrypted for securityPrice/performance and reduced time-to-market
ConsSampling causes loss of informationA/D and D/A requires mixed-signal hardwareLimited speed of processorsQuantization and round-off errors
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DSP APPLICATIONS
Image Processing Robotic vision, FAX,satellite weatherInstrumentation Spectrum analysis, noisereductionSpeech & Audio Speech recognition,equilizationMilitary Radar processing, missile guidance
Telecommunications Echo cancellation,video conferencing, VoIPBiomedical ECG analysis, patientmonitoringConsumer Electronics Cell phones, set topbox, video cameras
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DSP APPLICATIONS
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ANOTHER LOOK AT DSP APPLICATIONS
High-endWireless Base Station - TMS320C6000Cable modemgateways
Mid-endCellular phone - TMS320C540Fax/ voice server
Low endStorage products - TMS320C27Digital camera - TMS320C5000
Portable phonesWireless headsetsConsumer audioAutomobiles, toasters, thermostats, ...
I n c r e a
s i n g
C o s t
I n c r e a s i n g
v o l u m e
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ADVANTAGES OF DSP
Guaranteed Accuracy Accuracy onlylimited by bit lengthPerfect Reproducibility Nocomponent tolerances, no componentdrift due to temperature or ageGreater Flexibility Functions andalgorithms can be changed throughsoftwareSuperior Performance Adaptivefiltering, linear phase responseSome Data Naturally Digital Images,computer files
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DISADVANTAGES OF DSP
Speed and Cost ADC/DAC, uProcDesign Time Can be trickyFinite Word Length Issues
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KEY DSP OPERATIONS
ConvolutionCorrelationFiltering
TransformationsModulation
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CONVOLUTION
Many uses but a common use is determininga systems output if system input and systemimpulse response is known. For continuoussystem:
( ) ( ) ( ) ( )
=== d ht xd t h xt ht xt y )()()(
( )t x ( )t h ( ) ( ) ( )t ht xt y =
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DISCRETE CONVOLUTION
We may however have a computer samplinga signal so that we have discrete data.So instead of continuous integration processwe have discrete summation.
( ) ( ) ( ) ( ) ( ) ,2,1,0 ===
=nk n xk hnhn xn y
k
Practically speaking though we would havefinite sequences x(n) and h(n) of lengths N 1 and N
2respectively, so this is then:
( ) ( ) ( ) ( ) ( ) ( )
1
1,,1,0
21
1
0
+=
===
=
N N M with
M nk n xk hnhn xn yM
k
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CORRELATION
Correlation is essentially the same asconvolution (from a computationalstandpoint). You just dont flip anything.Instead of describing system output,correlation tells us information about thesignals.Cross-correlation function
Tells you a measure of similarities between twosignals.Application: Identifying radar return signals
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Signals
What is a signal? A signal is a function of independent
variables such as time, distance,
position, temperature, pressure, etc. Most signals are generated naturally but
a signal can also be generatedartificially using a computer
Can be in any number of dimensions(1D, 2D or 3D)
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Lecture 1 CE804 Autumn 2007/8 (copyright R.Palaniappan, 2008)
CLASSIFICATION OF SIGNALS
Signals can be classified into various types byNature of the independent variablesValue of the function defining the signals
Examples:Discrete/continuous functionDiscrete/continuous independent variableReal/complex valued functionScalar (single channel)/Vector (multi-channels)Single/Multi-trial (repeated recordings)Dimensionality based on the number of independent variables(1D/2D/3D)Deterministic/randomPeriodic/aperiodicEven/oddMany more.
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Lecture 1 CE804 Autumn 2007/8 (copyright R.Palaniappan, 2008)
CLASSIFICATION - DISCRETE/CONTINUOUSSIGNALS
Normally, the independent variable is time
Continuous time signal Time is continuousDefined at every instant of time
Discrete time signal Time is discreteDefined at discrete instants of time - it is a sequence of numbers
Four classifications based on time/amplitude -continuous/discrete:
Analogue, digital, sampled, quantised boxcar
CONTINUOUS AND DISCRETE
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CONTINUOUS AND DISCRETESIGNALS
Continous signal
xa(t)
Discrete signal(sequence)
x[n]
x[n] = xa(nT )
T : sampling period
f s = 1/ T : sampling rate
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Lecture 1 CE804 Autumn 2007/8 (copyright R.Palaniappan, 2008)
CLASSIFICATION - DISCRETE/CONTINUOUSSIGNALS (CONT)
Amplitude- continuous
Time-continuous
Amplitude- continuous
Time-discrete
Amplitude- discrete
Time-discrete
Amplitude- discrete
Time-continuous
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RANDOM V S DETERMINISTIC SIGNAL
Deterministic signalA signal that can be predicted using some methods like amathematical expression or look-up tableEasier to analyse
Random (stochastic)A signal that is generated randomly and cannot bepredicted ahead of timeMost biological signals fall in this categoryMore difficult to analyse
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Lecture 1 CE804 Autumn 2007/8 (copyright R.Palaniappan, 2008)
CLASSIFICATION PERIOD/APERIODIC
Periodic
Continuous time-signal isperiodic if it exhibitsperiodicity, i.e. x(t+T)=x(t),-
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Lecture 1 CE804 Autumn 2007/8 (copyright R.Palaniappan, 2008)
SINGULAR FUNCTIONSSingular functions
Important non-periodic signalsDelta/unit-impulse function is the most basic and all other singularfunctions can be derived from it
Unit impulse functions
Unit step functions
Unit ramp functions
Unit pulse function
== 1)(;0,0)( dt t t t 00
,0,1
{)(==
nn
n
00
,1,0
{)( >
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CLASSIFICATION EVEN/ODDEven signal
Signal exhibit symmetry inthe time domainx(t)=x(-t) or x(n)=x(-n)
Odd signalSignal exhibit anti-symmetryin the time domainx(t)=-x(-t) or x(n)=-x(-n)
A signal can be expressed as a sum of its even andodd components
x(t)=x even (t)+x odd (t)where x even (t)=1/2[x(t)+x(-t)], x odd (t)=1/2[x(t)-x(-t)]
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CLASSIFICATION OF SIGNALS
SIGNAL DESCRIPTION EXAMPLE
1 D Signal is a function of asingle independentvariable
Speech
2 - DSignal is a function of 2independent variables
Image
M - D Signal has more than 2independent variables
Video signal
DIMENSIONALITY
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CLASSIFICATION OF SIGNALS
Continuous-time signalsThe signal is defined forevery instant of time in adefined range
Discrete-time signalThe independent
variable (time) isdiscrete. The signal isdefined at discreteinstants of time
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CLASSIFICATION OF SIGNALS
Analog signalA continuous-timeand a continuous
amplitude
x(t)
t
x q(t) t
A Quantized Signal discrete in
amplitude butcontinuous in
time
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CLASSIFICATION OF SIGNALSSampled data signalhas a continuousamplitude. Amplitudecan take any valuewithin a specified
range.
Digital signal is adiscrete-time signalwith discrete-valuedamplitudes
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CLASSIFICATION OF SIGNALSA deterministic Signal
is one that isuniquely determinedby a well definedprocess such as amathematicalexpression or a look-up table
A random signal isone that isgenerated in arandom fashion andcannot be predicted
or reproduced
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Copyright 2001,S.K.Mitra
CLASSIFICATION OF SIGNALSDimension Type Symbol Independent
variable
1 - D Continuous-time v(t) t
1 - D Discrete - time {v(n)} n
2 - D Continuous-spatial v(x,y) x,y
2 - D Discrete - spatial {v(m,n)} m,n
3 - D Continuous-time and
spatial
v(x,y,t) x,y,t
3 - D Continuous-time andspatial
x,y,t
=),,(
),,(
),,(
),,(
t y xb
t y x g
t y xr
t y xu
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
Graphical representation of a discrete-timesignal with real-valued samples is as shownbelow:
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
)(t xa
In some applications, a discrete-timesequence { x [n ]} may be generated by
sampling a continuous-time signal atuniform intervals of time
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
Here, n -th sample is given by
The spacing T between two consecutive samples iscalled the sampling interval or sampling period
Reciprocal of sampling interval T , denoted as ,
is called the sampling frequency :
),()(][ nT xt xn x anT t a == = ,1,0,1,2, =n
T F
T F
T
1=
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
Unit of sampling frequency is cycles persecond , or hertz (Hz), if T is in seconds
Whether or not the sequence { x [n ]} has beenobtained by sampling, the quantity x [n ] iscalled the n -th sample of the sequence
{ x [n ]} is a real sequence , if the n -th sample x [n ] is real for all values of n
Otherwise, { x [n ]} is a complex sequence
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
A complex sequence { x [n ]} can be written as
where
andare the real and imaginary parts of x [n ]
The complex conjugate sequence of { x [n ]} is given by
Often the braces are ignored to denote a sequence if there is no ambiguity
][n xre][n x
im
]}[{]}[{]}[{ n x jn xn x imre +=
]}[{]}[{]}[*{ n x jn xn x imre =
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
Two types of discrete-time signals: - Sampled-data signals in which samples arecontinuous-valued- Digital signals in which samples arediscrete-valuedSignals in a practical digital signal processingsystem are digital signals obtained byquantizing the sample values either by rounding or truncation
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
A discrete-time signal may be a finite-length or an infinite-length sequence
Finite-length (also called finite-duration orfinite-extent ) sequence is defined only for afinite time interval:where and with
Length or duration of the above finite-length sequence is
21 N n N 1 N
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DISCRETE-TIME SIGNALS:DISCRETE-TIME SIGNALS:TIME-DOMAIN REPRESENTATIONTIME-DOMAIN REPRESENTATION
A length- N sequence is often referred to as anN-point sequence
The length of a finite-length sequence can be
increased by zero-padding , i.e., by appending itwith zeros
A right-sided sequence x [n ] has zero-valued
samples for
If a right-sided sequence is called acausal sequence
1 N n ,02 N
n N 1
2 N n
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OPERATIONS ON SEQUENCES:OPERATIONS ON SEQUENCES:BASIC OPERATIONS BASIC OPERATIONS
Product ( modulation ) operation:
Modulator
An application is in forming a finite-lengthsequence from an infinite-length sequence bymultiplying the latter with a finite-lengthsequence called a window sequence Process called windowing
x [n ] y [n ]
w [n ] ][][][ nwn xn y =
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BASIC OPERATIONSBASIC OPERATIONS
Addition operation:Adder
Multiplication operationMultiplier
][][][ nwn xn y +=
A
x [n ] y [n ]
][][ n x An y =
x [n ] y [n ]
w [n ]
+
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BASIC OPERATIONS BASIC OPERATIONS
Time-shifting operation:where N is an integer
(i) If N > 0 , it is delaying operation
Unit delay
(ii) If N < 0 , it is an advance operation
Unit advance
][][ N n xn y =
y [n ] x [n ] z
1 z y [n ] x [n ] ][][ 1= n xn y
][][ 1+= n xn y
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BASIC OPERATIONS BASIC OPERATIONS
Time-reversal ( folding ) operation:
Branching operation:Used to provide multiple copies of asequence
][][ n xn y =
x [n] x [n]
x [n]
ALIASING
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ALIASINGAliasing :
If you sample too slow, the high frequency components will become irregularnoise at the sampling frequency
They are noises that are in the same frequency range of your signal!!!
Look at the samples
alone Can you tell which of the two frequenciesthe sampled seriesrepresents?
Either of the twosignals could producethe samples, i.e., thesignals are aliasesof each other
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CLASSIFICATION OF SEQUENCES:CLASSIFICATION OF SEQUENCES:ENERGY AND POWER SIGNALS ENERGY AND POWER SIGNALS
Power Signal Power Sig nal An infinite energy signal with finite average power iscalled a power signal
Example - A periodic sequence which has a finite
average power but infinite energy
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Energy SignalsEnerg y Signals
A finite energy signal with zero averagepower is called an energy signal
Example - a finite-length sequence which hasfinite energy but zero average power
3( 1) ,[ ]
0, 0, 10
n others x n
n n
=<
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BASIC SEQUENCES
Unit impulse Unit step
Exponential
Periodic
Sinusoidal
Random
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BASIC SEQUENCESBASIC SEQUENCES
Unit sample sequence -
Unit step sequence -
=
= 0,0 0,1][ nnn 1
4 3 2 1 0 1 2 3 4 5 6n
Time-Invariant
=> Time-variant
=> Time-variant
=> Time-variant
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AliasingUnable to distinguish two continuous signals withdifferent frequencies based on samplesFrequencies higher than Nyquist frequency
Anti-aliasingLow-pass filter the frequencies above Nyquistfrequency
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DISCRETE-TIME SYSTEM
Discrete-time system has discrete-timeinput and output signals
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Discrete-time (DT) system is `sampled data system:Input signal u[k] is a sequence of samples (=numbers)
..,u[-2],u[-1],u[0],u[1],u[2],System then produces a sequence of output samples y[k]
..,y[-2],y[-1],y[0],y[1],y[2],
Will consider linear time-invariant (LTI) DT systems:Linear :
input u1[k] -> output y1[k]
input u2[k] -> output y2[k]hence a.u1[k]+b.u2[k]-> a.y1[k]+b.y2[k]
Time-invariant (shift-invariant)input u[k] -> output y[k], hence input u[k-T] -> output y[k-T]
u[k] y[k]
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Causal systems:iff for all input signals with u[k]=0,k output y[k]=0,k output ,0,0,h[0],h[1],h[2],h[3],...
General input u[0],u[1],u[2],u[3]: (cfr. linearity & shift-invariance!)
=]3[]2[]1[]0[
.
]2[000]1[]2[00]0[]1[]2[0
0]0[]1[]2[00]0[]1[000]0[
]5[]4[]3[]2[]1[]0[
uuuu
hhhhhh
hhhhh
h
y y y y y y
`Toeplitz matrix
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Convolution:
=
]3[
]2[
]1[]0[
.
]2[000
]1[]2[00
]0[]1[]2[0
0]0[]1[]2[00]0[]1[
000]0[
]5[
]4[
]3[
]2[]1[
]0[
u
u
uu
h
hh
hhh
hhhhh
h
y
y
y
y y
y
u[0],u[1],u[2],u[3] y[0],y[1],...
h[0],h[1],h[2],0,0,...
][*][][.][][ k uk hiuik hk yi
== = `convolution sum
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Z-Transform:
=
i
i z ih z H ].[)(
[ ] [ ]=
]3[]2[]1[ ]0[
.
]2[000]1[]2[00]0[]1[]2[0
0]0[]1[]2[ 00]0[]1[
000]0[
.1
]5[]4[]3[]2[ ]1[
]0[
.1
3211).()(
5432154321
uuuu
hhhhhh
hhh hh
h
z z z z z
y y y y y
y
z z z z z
z z z z H z Y
=
i
i z i y z Y ].[)( =
i
i z iu z U ].[)(
)().()( z U z H z Y = H(z) is `transfer function
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Z-Transform :input-output relationmay be viewed as `shorthand notation
(for convolution operation/Toeplitz-vector product)stability
bounded input u[k] -> bounded output y[k]--iff
--iff poles of H(z) inside the unit circle(for causal,rational systems)
)().()( z U z H z Y =
k
k h ][
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Example-1 : `Delay operator
Impulse response is ,0,0,0, 1,0,0,0, Transfer function is
Example-2 : Delay + feedback Impulse response is ,0,0,0, 1,a,a^2,a^3 Transfer function is
1)( = z z H
u[k]
y[k]=u[k-1]
x
+
a
u[k]
y[k]
1
1
11
433221
.1)(
)(.)(
......)(
=
=
++++=
z a z
z H
z z H z a z H
z a z a z a z z H
LINEAR TIME INVARIANT
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LINEAR TIME-INVARIANT (LTI) SYSTEM
Discrete-time system is LTI if itsinput-output relationship can be described by thelinear constant coefficients difference equation
The output sample y( ) might depend on all input samplesthat can be represented as
))(()( k x y =