EEE311:DigitalSignalProcessingICourseTeacher:Dr.NewazMd.SyfurRahim AssociatedProfessor, DeptofEEE,BUET,Dhaka1000.

Syllabus:AsmentionedinyourcoursecalendarReferenceBooks:

1. DigitalSignalProcessing:Principles,Algorithms,andApplicationsJohnG.Proakis2. DigitalSignalProcessing:APracticalApproachEmmanuelC.Ifeachor3. SchaumsOutlinesofDigitalSignalProcessing4. ModernDigitalSignalProcessingRobertoCristi

CourseOutlines:ThiscoursewillcoverChapter1through5ofProakissandChapter5through7ofIfeachorsbook.

SignalsSystemsandSignalProcessingAsignalisafunctionofoneormoreindependentvariablesthatusuallyrepresenttimeand/orspace.Asignalcontainssomekindof informationthatcanbeconveyed,displayed,ormanipulated.Examplesofsignalsofparticular interestsare:

Speech,whichweencounterintelephony,radio,andeverydaylife. Biomedicalsignals,suchaselectrocardiogram Soundandmusic,suchasreproducedbyCDplayer Videoandimage,whichpeoplewatchontelevision Radarsignals,whichareusedtodeterminetherangeandbearingofdistanttargets

A system is a practical device that performs an operation on a signal to modify the signal or extract additionalinformationfromit.Asystemmaybeelectrical,mechanical,thermal,hydraulicoranalgorithm.

By signal processingwemean the type of operations that is performed by the system to the signal.Digital signalprocessingisconcernedwiththedigitalrepresentationofsignalsandtheuseofdigitalprocessorstoanalyze,modify,orextractinformationfromsignals.ThesignalsusedinmostDSParederivedfromanalogsignalswhichhavebeensampledat regular intervals and converted into a digital form.DSP is now used inmany areaswhere analogmethodswerepreviouslyusedandinapplicationswhicharedifficultorimpossiblewithanalogmethod.

AdvantagesofDSPThemainattractionsofDSPareduetothefollowingadvantages:

Digitalsignalcanwithstandchannelnoiseanddistortionmuchbetterthananalogsignal. Repeaterscanbeusedforlongdistancedigitalcommunication Digitalsystemcanbeeasilymodifiedwithsoftwarethatimplementsthespecificapplications. Digitalsignalscanbecodedtoreduceerrorrate. Storageofdigitalsignaliseasyandinexpensiveanddoesnotdeterioratewithage. Reproductionofdigitalmessagesisextremelyreliablewithoutdistortion DSPallows sophisticatedapplications suchas speech recognitionand imagecompression tobe implemented

withlowpowerportabledevices Theaccuracyisonlydeterminedbythenumberofbitsused. Nodriftinperformancewithtemperatureorage LinearphaseresponsecanbeachievedandcomplexadaptivefilteringalgorithmscanbeimplementedusingDSP

techniques.

DSP designs can be expensivewhen large bandwidth signals are involved. TheADCs/DACsmay not have sufficientresolution forwide bandwidthDSP applications. In someDSP systems if an insufficient number of bits are used torepresentvariablesseriousdegradationinsystemperformancemayresult.

ApplicationsofDSPDSPhasrevolutionizedmanyareasofscienceandengineering.Theyaresummarizedbelow:

9 Measurements and analysis: Preconditioning the measured signal by rejecting the disturbing noise andinterference. The digital filters can be found in ECG and EEG equipment to record the weak signals in thepresenceofheavybackgroundnoiseandinterference.DSPtechniquesarealsousedfortheanalysisofradarandsonarechoes. InmostGPSreceiverstodayadvancedDSPtechniquesareemployedtoenhanceresolutionandreliability.[+patientmonitoring,Xraystorage,enhancement]

9 Telecommunications:DSP isused in telephone systems forDTMF (dualtonemultifrequency) signaling,echocancellingoftelephonelines,equalizersforhighspeedtelephonemodems,etc.Errorcorrectingcodesareusedtoprotectdigitalsignalsfrombiterrorsduringdatatransmissions.Datacompressionalgorithmsareutilizedtoreduce thenumberofdatabits torepresentgiven information.DSP isused forspeechcoding inGSM (globalsystemformobilecommunication)telephones,inmodulatorsanddemodulatorsetc.[+videoconferencing,datacommunication]

9 Audioandtelevision:Digitalsignalprocessing ismandatory inCDplayers,digitalaudiotape (DAT)anddigitalcompact cassette (DCC) recorder. Digital methods are also used in digital audio broadcasting (DAB). HDTVsystemsareutilizinglotsofdigitalimageprocessingtechniques.

9 Digital image processing: Digital image processing is used for restoring blurred or distorted images, datacompression, identificationandanalysisofpicturesandphotos. [+pattern recognition, satelliteweathermap,facsimile]

9 Automotive: In automotive business DSP is used for control purposes. For example, ignition and injectioncontrol system, intelligent suspension system, antiskid brakes, climate control systems, intelligent cruisecontrollers, airbag controllers etc. Some speech recognition and speech synthesis are being tasted inautomobiles.Experimentshavebeenperformedforbackgroundnoisecancellationincarsusingadaptivedigitalfilters.

BasicElementsofDSPSystemsTheblockdiagramofatypicalDSPsystemisshowninFigurebelow.

Theanaloginputfilterisusedtobandlimittheinputsignalbeforedigitizationtoreducealiasing.TheADCconvertstheanalog input signal into a digital form. The heart of the system is the digital processor (MotorolaMC68000, TexasInstruments TMS320C25). The digital processor may implement one of the several DSP algorithms, such as, digitalfiltering.Afterprocessingthesignalmaybestoredinacomputermemoryforlateruseoritmaybedisplayedgraphicallyonadisplayunit.Sampling

Sampling is the acquisition of a continuous signal at discrete time intervals. The sampled signal is continuous inamplitudebutdefinedonlyindiscretepointsintime.TheprocessisshowninFigureabove.Thesignalobtainedinthiswayiscalleddiscretetimesignalandisrepresentedas ( )x n . ( ) ( )ax n x nT= ; n < < where,Tisthesamplingperiod.Theinverseofitissamplingfrequency, sF .[ 1/ ]sF T=

Basicsignals1. Unitsampleorunitimpulse, ( )n

1 0( )

0 0n

nn

==

Note:AnyD.T.signalcanbeexpandedinto, ( ) ( ) ( )k

x n x k n k=

= .2. Unitstep, ( )u n

3. Sinusoidalsignals

Acontinuoustimesinusoidalsignalisdefinedas, 0( ) cos( )x t A t = + .Adiscretetimesinusoidisobtainedbysamplingacontinuoustimesinusoidwithsamplinginterval, sT as,

0 0( ) ( ) cos( ) cos( )s sx n x nT A nT A n = = + = + where, 00 0 0

2 2ss

FT fF = = = iscalledthedigitalfrequency.

4. Exponentialsignal, na (or ne where, a e= and j = + )

SomepeculiaritiesofdiscretetimesinusoidsTherearetwounexpectedpropertiesofdiscretetimesinusoidswhichdistinguishthemwithcontinuoustimesinusoids.

1. A continuoustime sinusoid isalwaysperiodic regardlessof its frequency, .ButaDiscretetime sinusoid isperiodiconlyif is 2 timessomerationalnumber.

2. Adiscretetimesinusoiddoesnothaveuniquewaveform foreachvalueof . In fact,discretetimesinusoidswith frequencies separated by the multiples of 2 are identical. Thus a sinusoid

0 0cos cos( 2 ) cos kn k n n = + = wherekisaninteger.Adiscretetimesinusoid 0( ) cos( )x n A n = + isperiodicwithperiod 0N ,if 0( ) ( )x n x n N= + .Applyingthisconditionweget, 0 0 2N m = or, 0

0

2 mN = . 0N andmareintegers.

1 0( )

0 0n

u nn=

Figureaboveshowsthreesinusoids,4cos ,cos and cos 0.8

4 17n n n .Theperiodoffirstandthesecondsinusoidsare8

and17respectively.Thethirdsinusoidisnotperiodic.

Fromthesecondpropertyitcanbesaidthatsinusoidalsignalhasuniquewaveformoverarangeof 2 .Wemayselectthis range tobe to ,0 to 2 , to3 etc.We shall select this range as to .We call this range as thefundamentalrangeoffrequencies.Thusasinusoidofanyfrequency isidenticaltosomesinusoidoffrequency f inthefundamentalrange to .Thus, cos(8.7 ) cos(0.7 )n n + = + and cos(9.6 ) cos( 0.4 )n n + = + .Therefore,thefrequency 8.7 isidenticaltothefrequency 0.7 inthefundamentalrange.Alsothefrequency 9.6 isidenticaltothefrequency 0.4 inthefundamentalrange.FurtherreductioninfrequencyrangeConsider, cos(9.6 ) cos( 0.4 ) cos(0.4 )n n n + = + = .Thisresultshowsthatasinusoidofanyfrequency canalwaysbeexpressedasasinusoidoffrequency f ,where

f liesinthefrequencyrange0to .Asystematicproceduretoreducethefrequencyofasinusoid cos( )n + istoexpress as, 2f m = + ; f andmisaninteger.NonuniquenessofdiscretetimesinusoidFigurebelowshowshowtwodifferentcontinuoustimesinusoidsofdifferentfrequenciesgenerateidenticaldiscretetimesinusoid.

HighestoscillationrateindiscretetimesinusoidTherateofoscillationofasinusoidincreasescontinuouslyas increasesfrom 0 to .Therateofoscillationdecreases

As increasesfrom to 2 .ThisisillustratedinFigureabove.Afrequency ( )x + actuallyappearsasthefrequency( )x .Samplingcontinuoustimesinusoidandaliasing

Iftwosequences 1 1 1( ) cos( )x n A n = + and 2 2 2( ) cos( )x n A n = + havefrequenciesandphasesrelatedby, 2 1 2 12 ,k = + = or, 2 1 2 12 ,k = + = withkan integer, then the twosinusoidalsequenceshave thesamesamples, i.e. 1 2( ) ( )x n x n= .This is illustrated inFigurebelow.

Here, 1 , 1 2 + , 1 and 1 2 + representsthesamesignalinthetimedomain.Ifwelimitthedigitalfrequency withintheinterval to then there is one to one correspondencebetween the signals and their frequency representation. Foreach frequency in the interval to the correspondingaliasesarealloutsidetheinterval to itself.Now,therangeofuniquedigitalfrequencies,

T Or, / /T T or, s sF F Or,

2 2s s

This implies that the highest frequency of an analog signalmust be less than half the sampling frequency to avoidaliasing.

0

0

0

15 or 8 8

7 or 4 4

3 or 2 2

=

=

=