subathra_scilab4dsp.pdf

for Digital Signal Processing

SSubathraProjectEngineer,NRCFOSSAUKBCResearchCentreMITCampusofAnnaUniversityChennai600044subathra@aukbc.org

AICTESDPonOpenSourceSoftware,PSGTech,June22nd,2007July6th,2007

Scilab for Digital Signal Processing 2

Plan for PresentationTutorialSession

SignalProcessingwithScilab45mins(Tutor)

LabSession InstallationDemo 10mins(Tutor) InstallationofScilab 15mins(Participants) ScilabBuildinDemo 50mins(Participants) HandsonPractise 60mins(Participants)


Tutorial Session


Outline Scilab SignalProcessing Handlingvectors&matrices Usingplotfunctions Signalgeneration Sampling Convolution Correlation DiscreteFourierTransform DigitalFilterDesign


Scilab

Freesoftware Numericalprogramming RapidPrototyping Extensivelibrariesandtoolboxes Easyformatrixmanipulation


Scilab

Freesoftware Numericalprogramming RapidPrototyping Extensivelibrariesandtoolboxes Easyformatrixmanipulation

IdealforSignalProcessing


Signal Processing Asignalcarriesinformation,andtheobjectiveofsignal

processingistoextractusefulinformationcarriedbythesignal.

Themethodofinformationextractiondependsonthetypeofsignalandthenatureoftheinformationbeingcarriedbythesignal.

SignalProcessingisconcernedwiththemathematicalrepresentationofthesignalandthealgorithmicoperationcarriedoutonittoextracttheinformationpresent.


Signal Processing A1Dsignalisafunctionofasingleindependentvariable.

Eg:SpeechSignal=>time A2Dsignalisafunctionofatwoindependentvariable.

Eg:Image(likephotograph)=>twospatialvariables AMDsignalisafunctionofmorethanonevariable.

Eg:Eachframeofablackandwhitevideosignalisa2Dimagesignalthatisafunctionoftwodiscretespatialvariables,witheachframeoccurringsequentiallyatdiscreteinstantsoftime.=>twospatialvariables&time


Signal Processing Therepresentationofthesignalcanbeintermsofbasis

functionsinthedomainoftheoriginalindependentvariable(s),oritcanbeintermsofbasisfunctionsinatransformeddomain.

Asignalcanbegeneratedbyasinglesourceorbymultiplesources. SingleSource=>Scalar MultipleSource=>Vector


Signal Processing Therepresentationofthesignalcanbeintermsofbasis

functionsinthedomainoftheoriginalindependentvariable(s),oritcanbeintermsofbasisfunctionsinatransformeddomain.

Asignalcanbegeneratedbyasinglesourceorbymultiplesources. SingleSource=>Scalar MultipleSource=>Vector

HowtoprocessvectorswithScilab


Handling vectors Tocreateazerovectorwith20dimensions>a=zeros(1,20);

Tocreateavectorandstoreitinavariable>b=[12351];

Toextracttheelement1to3oftheabovevector>b(1:3)[123]


Handling matrices Toinitializematrix>m=zeros(3,3);>k=rand(3,3);>h=[1467;4321;143

8];

Toextracttheelementsofthematrix

>h(2:3,2:4)|178||215|

Togetthesizeofmatrix>size(h)>[34]

Transposeofamatrix>h=[1467;4321;143

8];>h|129||412||671||785|


Operator Notation Tomultiplytwomatricesaandb>a*b

Formultiplyingtransposeofmatrixawithitself>a*a

Forelementwisemultiplicationandaddition>c=a.*b>c=a.+b


Using Plot Function Plotfunctionisusedto

producenumberoftwodimensionalplots

Togeneratesarandomvectoroflength10andplotsthepointswithstraightlinejoiningeachpoints

>y=rand(1,10);>plot(y);

1 2 3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Fig.1PlotFunctionSample1


Using Plot Function color Colorofthelinejoiningthe

pointschangedusingaparameter yyellow ccyan ggreen wwhite mmagenta rred bblue kblack

>y=rand(1,10);>plot(y,r);

1 2 3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9



Using Plot Function

Toproduceadiscontiniousplot .usesdotateachpoint *usesasterisksateachpoint dusesblankdiamondateach

point ^usesupwardtrianglesateach

point ousescircleateachpoint +usescrossateachpoint vusesinvertedtriangleateach

point

>y=rand(1,10);>plot(y,r);

1 2 3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9



Using Plot Function subplot Severalplotscanbeaccommodatedinasinglefigurewindow

usingsubplotcommand.

Thiscommandtakesthreeparametersasinput,firsttwoparametersspecifiesthegridsize,i.e.howmanyrowsandcolumnsandthethirdparameterspecifiesthepositionoftheplotinthegrid.

Fore.g.,subplot(3,2,2)tellsscilabthatthefigurewindowisdividedasthreerows,two

columnsandtheplothastobeplacedinthesecondcolumnofthefirstrow.


Using Plot Function subplotExample:x1=rand(1,10);subplot(2,2,1);plot(x1);x2=rand(1,20);subplot(2,2,2);plot(x2);x3=rand(1,15);subplot(2,2,3);plot(x3);x4=rand(1,25);subplot(2,2,4);plot(x4);

1 2 3 4 5 6 7 8 9 100.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 2 4 6 8 10 12 14 16 18 200.00.10.20.30.40.50.60.70.80.91.0

0 2 4 6 8 10 12 14 160.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 5 10 15 20 250.00.10.20.30.40.50.60.70.80.91.0



Using Plot Function - label

Tomarklabel,thefunctiongcareturnsthehandleforthecurrentaxes

t=1:1:50y=rand(1,50);plot(t,y);a=gca();a.x_label.text=time;a.y_label.text=amplitude;

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

time

amplitud

e



Using Plot Function - Mesh plot

Meshplotcanbegeneratedusingplot3dcommand.

m=rand(5,7);i=1:1:5;j=1:1:7;plot3d(i,j,m);

0

1

Z

1

2

3

4

5

X

1

2

3

4

5

6

7

Y



Signal generation//sinewavet=0:0.01:3.14;y=sin(2*3.14*t);subplot(2,1,1);a=gca();a.x_label.text="Time";a.y_label.text="Amplitude";plot2d(t,y);xtitle("SineWaveGeneration");

//coswavet=0:0.01:3.14;y=cos(2*3.14*t);subplot(2,1,2);a=gca();a.x_label.text="Time";a.y_label.text="Amplitude";plot2d(t,y);xtitle("CosineWaveGeneration");

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.00.80.60.40.20.00.20.40.60.81.0

SineWaveGeneration

Time

Amplitud

e

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.00.80.60.40.20.00.20.40.60.81.0

CosineWaveGeneration

Time

Amplitud

e

Fig.7Signalgeneration


Sampling

Theprocessinwhichtheanalogcontinuoussignalaremeasuredatequalintervaloftimeandfinallyadiscretizedsetofdigitalnumbersarecreated.

ForpropersamplingofanalogsignalNyquistShannonsamplingtheoremshouldbesatisfied,i.e.samplingfrequencyshouldbeagreaterthantwicethemaximumfrequencyoftheinputsignal.


Sampling - Examplefo=input('Frequencyofsincewaveinhz=');ft=input('Samplingfrequencyinhz=');t=0:0.01:1;T=1.0/ft;x=sin(2*3.14*fo*t);subplot(2,1,1);a=gca();a.x_label.text="Time";a.y_label.text="Amplitude";plot(t,x);xtitle("Continuoussignal");

n=0:ft;y=sin(2*3.14*fo*n*T);subplot(2,1,2);a=gca();a.x_label.text="Time";a.y_label.text="Amplitude";plot2d3(n,y);xtitle("SampledSignal");

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.01.00.80.60.40.20.00.20.40.60.81.0

Continuoussignal

Time

Amplitud

e

0 5 10 15 20 25 30 35 40 45 501.00.80.60.40.20.00.20.40.60.81.0

SampledSignal

Time

Amplitud

e

Fig.8Sampling


Convolution

ConvolutionistheprocessinwhichtheresponseofaLTIsystemiscomputedforaninputsignal.

TheLTIsystemcanbedefinedusingtheimpulseresponseofthesystem.

Convolutionoftheinputsignalandimpulseresponseofthesystemgivestheoutputsignal.Thisprocessisalsocalleddigitalfiltering.

Mathematically,


Correlation

Correlationtakestwosignalsasinputandproducesthirdsignalasoutput.

Ifboththeinputsignalsareoneandthesame,thenitiscalledasautocorrelation

Ifboththeinputsignalsaredifferent,thenitiscalledascrosscorrelation

Correlationisusedtomeasurethesimilaritybetweenthetwoinputsignalsatthatparticulartime.

Mathematically,


Discrete Fourier Transform

Usedforanalysingthefrequencycomponentsofasampledsignal

DFTdecomposestheinputsignalintosetofsinusoids

InDFT,wetakeasequenceofrealnumbers(sampledsignal)asinputanditistransformedintoasequenceofcomplexnumbers.

Mathematically,


Digital Filter Design Analog & Digital FilterUsedtoremovetheunwantedsignalfromthe

usefulsignal. Foreg,removingnoisefromaudiosignal

TwotypesAnalog&Digitalfilters Analogfiltersusesinductors,capacitorstoproduce

therequiredeffects Digitalfilterusesmodernprocessorsfordoingthe

same


Digital Filter Design FIR & IIR

Digitalfiltersareclassifiedasnonrecursivefilters(FIR)andrecursivefilters(IIR) FIRFiltertheoutputwillbedependentonthecurrent&previousinputvalues

IIRFilterdependentonpreviousoutputinadditiontotheinputvalues


FIR LPF//Lowpassfilterfp=input('Enterthecutofffrequencyin

Hzfp=');n=input('Entertheorderofthefilter

n=');F=input('EntersamplingfrequencyinHz

F=');wc=fp/F;[coeffval,famp,ffreq]=wfir('lp',n,[wc0],

'hm',[00]);//frequencyresponseofthefilterplot2d(ffreq,famp);a=gca();a.x_label.text="Frequency";a.y_label.text="Magnitude";xtitle("FIRlowpassfilter");

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500.0

0.2

0.4

0.6

0.8

1.0

1.2

FIRlowpassfi l ter

Frequency

Magn

itude

Fig.9FIRLPF


FIR HPF//Highpassfilterfp=input('Enterthecutofffrequencyin

Hzfp=');n=input('Entertheorderofthefilter

n=');F=input('EntersamplingfrequencyinHz

F=');wc=fp/F;[coeffval,famp,ffreq]=wfir('hp',n,[wc0],

'hm',[00]);//frequencyresponseofthefilterplot2d(ffreq,famp);a=gca();a.x_label.text="Frequency";a.y_label.text="Magnitude";xtitle("FIRhighpassfilter");

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

FIRhighpassfil ter

Frequency

Magn

itude

Fig.10FIRHPF


IIR LPF//Lowpassfilterfp=input('EnterthecutofffrequencyinHz

fp=');n=input('Entertheorderofthefiltern=');F=input('EntersamplingfrequencyinHz

F=');wc=fp/F;hz=iir(3,'lp','butt',[wc0],[00]);[hzm,fr]=frmag(hz,256);plot2d(fr',hzm');a=gca();a.x_label.text="Frequency";a.y_label.text="Magnitude";xtitle('DiscreteIIRfilterlowpass');q=poly(0,'q');//toexpresstheresultintermsof

the...hzd=horner(hz,1/q)//delayoperatorq=z^1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500.0

0.2

0.4

0.6

0.8

1.0

1.2

DiscreteIIRfi l terlowpass

Frequency

Magn

itude

Fig.11IIRLPF


IIR HPF//Highpassfilterfp=input('EnterthecutofffrequencyinHz

fp=');n=input('Entertheorderofthefiltern=');F=input('EntersamplingfrequencyinHz

F=');wc=fp/Fhz=iir(3,'hp','butt',[wc0],[00]);[hzm,fr]=frmag(hz,256);plot2d(fr',hzm');a=gca();a.x_label.text="Frequency";a.y_label.text="Magnitude";xtitle('DiscreteIIRfilterhighpass');q=poly(0,'q');//toexpresstheresultintermsof

the...hzd=horner(hz,1/q)//delayoperatorq=z^1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500.0

0.2

0.4

0.6

0.8

1.0

1.2

DiscreteIIRfi lterhighpass

Frequency

Magn

itude

Fig.12IIRHPF


Reference

[1]JohnG.ProakisandDimitrisG.Manolakis,DigitalSignalProcessingprinciples,algorithms,andapplicationsThirdedition.

[2]SanjitK.Mitra,DigitalSignalProcessingacomputerbasedapproachSecondedition.

[3]ScilabDocumentation,Availableatwww.scilab.org


Lab Session


Scilab Installation How To Gotowww.scilab.org Checkforthelatestdownloadableversionofscilab(i.e.scilab

4.1.1.bin.linuxi686.tar.gz)anddownloadit. Untarthescilab4.1.1.bin.linuxi686.tar.gzusingthecommand

#tarxzvfscilab4.1.1.bin.linuxi686.tar.gzwherexreferstoextract,zreferstogzip,vreferstoverbose,freferstofile

RunScilabbyexecutingscilab(shellscriptinbin)


Scilab Build-in Demo

Scilabdemonstration

http://www.scilab.org/doc/demos_html/index.html

MatlabandScilabfunctions

http://www.scilab.org/product/dicmatsci/M2SCI_doc.htm


More about DSP

SignalProcessingInformationBase(SPIB)

http://spib.rice.edu/spib.html

DSPOnlineClasses

http://bores.com/index_dsp.htm

http://bores.com/index_online.htm

subathra_scilab4dsp.pdf

Documents