EE8591 Digital Signal Processing Unit -1

EE8591 UNIT I

1. UNIT-1
EE8591-Digital Signal
Processing

2. UNIT I INTRODUCTION
Classificationofsystems:Continuous,discrete,linear,causal,stability,dynamic,recursive,timevariance;
classificationofsignals:continuousanddiscrete,energyandpower;mathematicalrepresentationof
signals;spectraldensity;samplingtechniques,quantization,quantizationerror,Nyquistrate,aliasing
effect.
UNIT II DISCRETE TIME SYSTEM ANALYSIS
Z-transformanditsproperties,inversez-transforms;differenceequation–Solutionby
ztransform,applicationtodiscretesystems-Stabilityanalysis,frequencyresponse–Convolution–
DiscreteTimeFouriertransform,magnitudeandphaserepresentation
UNIT III DISCRETE FOURIER TRANSFORM & COMPUTATION
DiscreteFourierTransform-properties,magnitudeandphaserepresentation-ComputationofDFTusing
FFTalgorithm–DIT&DIFusingradix2FFT–Bu
UNIT IV DESIGN OF DIGITAL FILTERS
Need and choice of windows –Linear phase characteristics. Analog filter design –Butterworth and
Chebyshevapproximations; IIR Filters, digital design using impulse invariant and bilinear transformation
Warping, pre warping.
UNIT V DIGITAL SIGNAL PROCESSORS
Introduction –Architecture –Features –Addressing Formats –Functional modes -Introduction to
Commercial DS Processors
SYLLABUS

3. TEXT BOOKS:
1. J.G. Proakis and D.G. Manolakis, ‘Digital Signal Processing Principles, Algorithms and
Applications’, Pearson Education, New Delhi, PHI. 2003.
2. S.K. Mitra, ‘Digital Signal Processing –A Computer Based Approach’, McGraw Hill
Edu, 2013.
3. Lonnie C.Ludeman ,”Fundamentals of Digital Signal Processing”,Wiley,2013
REFERENCES
1. Poorna Chandra S, Sasikala. B ,Digital Signal Processing, Vijay Nicole/TMH,2013.
2. Robert Schilling & Sandra L.Harris, Introduction to Digital Signal Processing using
Matlab”, Cengage Learning,2014.
3. B.P.Lathi, ‘Principles of Signal Processing and Linear Systems’, Oxford University
Press, 2010 3. Taan S. ElAli, ‘Discrete Systems and Digital Signal Processing with
Mat Lab’, CRC Press, 2009.
4. SenM.kuo, woonseng…s.gan, “Digital Signal Processors, Architecture,
Implementations & Applications, Pearson,2013
5. DimitrisG.Manolakis, Vinay K. Ingle, applied Digital Signal
Processing,Cambridge,2012

4. Define signal
Asignalisadescriptionofhowoneparametervarieswithanotherparameter.
Forinstance,voltagechangingovertimeinanelectroniccircuit,orbrightness
varyingwithdistanceinanimage.Asystemisanyprocessthatproduces
anoutputsignalinresponsetoaninputsignal.

5. Cont/.,
•flow of information
•measured quantity that varies with time (or position)
•electrical signal received from a transducer
•(microphone, thermometer, accelerometer, antenna,
etc.)
•electrical signal that controls a process
•Continuous-time signals: voltage, current, temperature,
speed, . . .
•Discrete-time signals: daily minimum/maximum
temperature,

6. Define Digital,Signal,Processing
&System
•Digital:Indigitalcommunication,weusediscretesignalstorepresentdata
usingbinarynumbers.
•Signal:Asignalisanythingthatcarriessomeinformation.It’saphysical
quantitythatconveysdataandvarieswithtime,space,oranyother
independentvariable.Itcanbeinthetime/frequencydomain.Itcanbeone-
dimensionalortwo-dimensional.
•Processing:Theperformingofoperationsonanydatainaccordancewith
someprotocolorinstructionisknownasprocessing.
•System:Asystemisaphysicalentitythatisresponsiblefortheprocessing.
Ithasthenecessaryhardwaretoperformtherequiredarithmeticorlogical
operationsonasignal.

7. Difference between Analog and digital
signal
•AnalogSignals
•Theanalogsignalswereusedinmanysystemstoproducesignalstocarry
information.Thesesignalsarecontinuousinbothvaluesandtime.Theuse
ofanalogsignalshasbeendeclinedwiththearrivalofdigitalsignals.In
short,tounderstandtheanalogsignals–allsignalsthatarenaturalorcome
naturallyareanalogsignals.
•DigitalSignals
•Unlikeanalogsignals,digitalsignalsarenotcontinuous,butsignalsare
discreteinvalueandtime.Thesesignalsarerepresentedbybinarynumbers
andconsistofdifferentvoltagevalues.

8. Cont.,

9. Signal processing
Signals may have to be transformed in order to
Amplify or filter out embedded information
Detect patterns
Prepare the signal to survive a transmission channel
Prevent interference with other signals sharing a medium
Distortions contributed by a transmission channel
Compensate for sensor deficiencies
Find information encoded in a different domain

10. Digital signal processing
•Digital Signal Processing is the process of representing signals
in a discrete mathematical sequence of numbers and analyzing,
modifying, and extracting the information contained in the
signal by carrying out algorithmic operations and processing
on the signal

11. Block Diagram of a Digital Signal
Processing System

12. Digital signal processing
Advantages:
•noise is easy to control after initial quantization
•highly linear (within limited dynamic range)
•complex algorithms fit into a single chip
•flexibility, parameters can easily be varied in software
•digital processing is insensitive to component tolerances, aging,
•environmental conditions, electromagnetic interference
Applications:
•Communication systems
•Consumer electronics
•Music
•Medical diagnostics
•Aviation

13. Continuous Time (CT) Signals
•Most of the signals in the physical world are CT signals, since the time
scale is infinitesimally fine (e.g., voltage, pressure, temperature,
velocity).
•Often, the only way we can view these signals is through a transducer, a
device that converts a CT signal to an electrical signal.
•Common transducers are the ears, the eyes, the nose… but these are a
little complicated.
•Simpler transducers are voltmeters, microphones, and pressure sensors.

14. contin/;

15. Discrete-Time (DT) Signals
•Wecanwriteacollectionofnumbers(1,-3,7,9)representinga
signalasafunctionofadiscretevariable,n.x[n]representsthe
amplitude,orvalueofthesignalasafunctionofn,whichtakes
onintegervalues
•Manyhuman-generatedsignalsarediscrete(e.g.,MIDIcodes,
stockmarketprices,digitalimages).
•Inthiscourse,wewillshowthatmostofthepropertiesthatapply
toCTsignalsapplyinasimilarmannertoDTsignals

16. contin/;

17. DEFINE ENERGY AND POWER
SIGNAL

18. ENERGY AND POWER SIGNAL

19. ENERGY AND POWER SIGNAL

20. Representation of discrete time signals
Graphical representation
Functional representation
Tabular representation
Sequence representation

21. Graphical representation

22. Functional representation

23. Tabular representation

24. Sequence representation

25. Classification of Discrete-time
Systems
•Static and dynamic systems
•causal and non causal systems
•Linear and non linear systems
•Time in variant and time varying systems
•stable and unstable systems
•Invertible and non invertible systems
•FIR and IIR systems

26. •Memorylesssystems:Iftheoutputofthesystematan
instantnonlydependsontheinputsampleatthat
time(andnotonpastorfuturesamples)thenthe
systemiscalledmemorylessorstatic,
e.g.y(n)=ax(n)+bx
2
(n)
Otherwise,thesystemissaidtobedynamicorto
havememory,
e.g.y(n)=x(n)−4x(n−2)
Static and dynamic systems

27. Example1:
Answer:
i) Dynamic
ii) Static
iii) Dynamic

28. •In a causal system, the output at any time nonly
depends on the present and past inputs.
•An example of a causal system:
y(n)=F[x(n),x(n−1),x(n− 2),...]
•All other systems are non-causal.
•A subset of non-causal system where the system
output, at any time nonly depends on future inputs is
called anti-causal.
y(n)=F[x(n+1),x(n+2),...]
Causal vs. Non-causal Systems

29. Example2:
Answer:
i) Causal
ii) Causal
iii) Non Causal

30. •Unstable systems exhibit erratic and extreme
behavior. BIBO stable systems are those
producing a bounded output for every bounded
input:
Example:
i)y(n)=x(n
2
)---------stable
ii)y(n)=n.x(n)-------unstable
Stable vs. Unstable Systems
yx MnyMnx )()(

31. •Superposition principle:T[ax
1(n)+bx
2(n)]=aT[x
1(n)]+bT[x
2(n)]
•A relaxed linear system with zero input
produces a zero output.
Linear vs. Non-linear Systems
Scaling property
Additivity property

32. •Example:
•Solution:
Example:
Linear vs. Non-linear Systems)()(
2
nxny )()(
2
11
nxny
Linear or non-linear?)()(
2
22
nxny )()())()(()(
2
22
2
1122113
nxanxanxanxaTny  )()()()(
2
22
2
112211
nxanxanyanya 
Linear!)(
)(
nx
eny 1)(0)(  nynx
Non-linear!
Useful Hint: In a linear system, zero input results in a zero
output!

33. i)y(n)=x(2n)
ii)y(n)=cosx(n)
Answer:
i)Linear
ii) Non linear
Example 3:

34. •Time-invariant example: differentiator
•Time-variant example: modulator
Time-invariant vs. Time-variant Systems)1()()()(  nxnxnynx
T )2()1()1()1(  nxnxnynx
T ).().()()(
0
nCosnxnynx
T
 x(n-1)
T
¾®¾x(n-1).Cos(w
0.n) y(n-1)=x(n-1).Cos(w
0.(n-1)) ¹y(n-1)

35. EXAMPLE 4:
Answer:
i) Time invariant
ii) Time Variant
iii) Time invariant

36. •LTI systems have two important characteristics:
–Time invariance: A system Tis called time-invariant or shift-
invariant if input-output characteristics of the system do not
change with time
–Linearity: A system Tis called linear iff
•Why do we care about LTI systems?
–Availability of a large collection of mathematical techniques
–Many practical systems are either LTI or can be approximated by LTI
systems.
Linear Time-Invariant (LTI) Systems
36 )()()()( knyknxnynx
TT

T[ax
1(n)+bx
2(n)]=aT[x
1(n)]+bT[x
2(n)]

37. Impulse Response of LTI Systems
h(n): the response of the LTI system to the input unit sample (n), i.e.h(n)=T((n))
An LTI system is completely characterized by a single impulse response h(n).y(n)=T[x(n)]= )(*)()()( nhnxknhkx
k



Response of the system to the input
unit sample sequence at n=k
Convolution
sum
37
Hossein Sameti, CE, SUT, Fall 1992

38. Sampling techniques
•Therearethreetypesofsamplingtechniques:
•Impulsesampling.
•Naturalsampling.
•FlatTopsampling.

39. Quantization
•Quantization,inmathematicsanddigitalsignal
processing,istheprocessofmappinginputvaluesfrom
alargeset(oftenaontinuousset)tooutputvaluesina
(countable)smallerset,oftenwithafinitenumberof
elements.Roundingandtruncationaretypical
examplesofquantizationprocesses
•Quantizationerroristhedifferencebetweenthe
analogsignalandtheclosestavailabledigitalvalueat
eachsamplinginstantfromtheA/D
converter.Quantizationerroralsointroducesnoise,
calledquantizationnoise,tothesamplesignal.