dsp laboratory experiments

8/13/2019 DSP Laboratory Experiments

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n &-:-8%x & ,a ;n%a&gca, %a.thic5ness & 2%

plot2d3,4gnn4#n#xxtitle,46raphical $epresentation of Exponentially "ncreasing Signal4#4n4#4x*n/4 %

esult

Ex.pt.No'! inear an *ircular *on+olution of t,o sequencesAim: To perform Linear


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clc%clear all%close %x & inp t,4enter x seq4 %h & inp t,4enter h seq4 %m & length,x %n & length,h %((?ethod - !sing Direct


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(($es lt((enter x seq *- - - -/((enter h seq *- 2 3/((


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x2 & *-#2#3#'/% //Second sequencem & length,x- % //length of first sequencen & length,x2 % //length of second sequence

//To make length of x1 and x are !qualif ,m Fn for i & n7-:m x2,i & 8% endelseif ,nFm for i & m7-:n x-,i & 8% endend

N & length,x- %

x3 & +eros,-#N % //x" # Circular convolution result initiali$ed to $erosa,- & x2,- %for & 2:N a, & x2,N) 72 %endfor i &-:N x3,- & x3,- 7x-,i Ca,i %endG,-#: &a%

//Calculation of circular convolutionfor 5 & 2:N for &2:N x2, & a, )- % end x2,- & a,N % G,5#: & x2% for i & -:N a,i & x2,i % x3,5 & x3,5 7x-,i Ca,i %

endenddisp,G#4


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// 1( )( "( ( // ( 1( )( "( // "( ( 1( )( // )( "( ( 1( // // Circular Convolution %esult x"&n' # // // 1)( 1*( 1)( 1*(

Ex.pt.No'" *ircular con+olution using

Aim: To perform circ lar con=ol tion of t>o seq ences sing @@T)"@@T method.

//Caption: Performing Circular Convolution +sing FFT,-FFT method clear%clc%close%L & '% //.ength of the Sequence

N & '% // ,point 0FT 10


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x- & *2#-#2#-/%x2 & *-#2#3#'/%

//Computing 0FTG- & fft,x-#)- %G2 & fft,x2#)- %disp,G-#4D@T of x-*n/ is G-,5 &4disp,G2#4D@T of x-*n/ is G2,5 &4

//Multiplication of 0FTsG3 & G-.CG2%disp,G3#4D@T of x3*n/ is G3,5 &4

//Circular Convolution %esult x3 &abs,fft,G3#-disp,x3#4


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h & *-#2#3/% //-mpulse %esponse of .T- S6stemx & *-#2#2#-/% //-nput %esponse of .T- S6stem

N- & length,x % N2 & length,h % N & N-7N2)-disp,N#4Length of tp t $esponse y,n 4

//Padding $eros to Make .ength of 7h7 and 7x7 //!qual to length of output response 767 h- & *h#+eros,-#N)N2 /%x- & *x#+eros,-#N)N- /%

//Computing FFTH & fft,h-#)- %G & fft,x-#)- %

//Multiplication of 0FTs

I & G.CH //.inear Convolution %esult y &abs,fft,I#-disp,G#4D@T of i(p G,5 &4disp,H#4D@T of imp lse seq ence H,5 &4disp,I#4D@T of Linear @ilter o(p I,5 &4disp,y#4Linear


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// .inear Convolution result 6&n'# // // 1( )( >( 11(


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x & *-#2#3#'/% //Computing 0FTG & fft,x#)- %disp,G#4@@T of x*n/ is G,5 &4x &abs,fft,G#-disp,x#4"@@T of G,5 is x*n/&4

//Plotting the spectrum of 0iscrete Sequences bplot,2#-#-a&gca, %a.data0bo nds&*8#8% #-8/%

plot2d3,4gnn4#8:length,x )-#x b & gce, % b.children,- .thic5ness &3%xtitle,46raphical $epresentation of Discrete Seq ence4#4n4#4x*n/4 %

s bplot,2#-#2a&gce, %a.data0bo nds&*8#8% #-8/%

plot2d3,4gnn4#8:length,G )-#abs,G b & gce, % b.children,- .thic5ness &3%xtitle,46raphical $epresentation of Discrete Spectr m4#454#4G,5 4 %

//%esult //FFT of x&n' is 2k3# // 14( , ( 5 (i , ( , ( , (i // //-FFT of 2k3 is x&n'# // 1( ( "( )(

esult

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Ex.pt.No'/ ime an requenc$ esponse of & s$stems

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Aim: To >rite a scilab program in order to generate and plot the imp lse responseand freq ency response of a first order Linear


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s bplot,2#-#- %a & gca, %a.y0location & 1origin1%

plot,J#HJ0?ag %xlabel,4@req ency in $adians(Seconds)))F J4 %ylabel,4abs,H, J 4title,4?agnit de $esponse4

//Plotting Phase %eponses bplot,2#-#2 %a & gca, %a.y0location & 1origin1%a.x0location & 1origin1%

plot,J#HJ0PhaseCKpi(-M8 %xlabel,4 @req ency in $adians(Seconds)))F J4 %

ylabel,4 9H, J 4title,4Phase $esponse in $adians4

esult

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Ex.pt.No' Sampling2 3erification of Sampling an Effect ofaliasing

Aim: To >rite a scilab program in order to con=ert a contin o s time signal ,


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s bplot,2#-#- %a &gca, %a.x0location & 1origin1%a.y0location & 1origin1%

plot,t#xa %xlabel,4t in sec.4 %ylabel,4xa,t 4title,4 riginal Analog Signal4s bplot,2#-#2 %a &gca, %a.x0location & 1origin1%a.y0location & 1origin1%xlabel,4t in sec.4 %ylabel,4xa,t 4

title,4$econstr cted Signal sing sinc f nction# @s & -88H+4 % plot,t#Ga %

Sinc unction

f nction * $/&sinc0ne>, xi&find, x&&8 %x,i & -% // don7t need this is /4 Darning is off$ & sin,KpiC x .(,KpiCx %

$,i & -%

endf nction

esult

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Ex.pt.No'? Design of & ilters (@in o, Design anrequenc$ Sampling)

(?).a & ilter -@in o, Base Design

Aim: To design Jindo>)based @"$ Lo> Pass @ilter# High Pass @ilter# and Pass@ilter and and Stop @ilter sing gi=en desired freq ency response.

Program 1' & o, Pass ilter

//Caption: Program to 0esign F-% .oD Pass Filter clc%close%

? & inp t,4Enter the dd @ilter Length &4 % //Filter lengthJc & inp t,4Enter the Digital < toff freq ency &4 % //0igital Cutoff frequenc6T o & ,?)- (2 //Center Galuefor n & -:? if ,n && T o7- hd,n & Jc(Kpi% else hd,n & sin,JcC,,n)- )T o (,,,n)- )T o CKpi % endend

//%ectangular EindoDfor n & -:? J,n & -%end

//EindoDing Filter Coefficientsh & hd.CJ%disp,h#4@ilter


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plot,2Cfr#h+m0dxlabel,4Normali+ed Digital @req ency J4 %ylabel,4?agnit de in d 4 %title,4@req ency $esponse 8f @"$ LP@ sing $ectang lar >indo>4xgrid,-

//%esult //!nter the 8dd Filter .ength # ; //!nter the 0igital Cutoff frequenc6 # Hpi/ // // Filter Coefficients are // // , 4(14*14"" // 1(>)>0,1; # 4(4 // 4("1


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Program !' & ;ig8 Pass ilter

//Caption: Program to 0esign F-% 9igh Pass Filter clear%clc%close%? & inp t,4Enter the dd @ilter Length &4 % //Filter lengthJc & inp t,4Enter the Digital < toff freq ency &4 % //0igital Cutoff frequenc6T o & ,?)- (2 //Center Galuefor n & -:? if ,n && T o7- hd,n & -)Jc(Kpi% else hd,n & ,sin,KpiC,,n)- )T o )sin,JcC,,n)- )T o (,,,n)- )T o CKpi % endend

//%ectangular EindoD

for n & -:? J,n & -%end

//EindoDing Fitler Coefficientsh & hd.CJ%disp,h#4@ilter


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Program "' & Ban Pass ilter

//Caption: Program to 0esign F-% Iand Pass Filter clear%clc%close%? & inp t,4Enter the dd @ilter Length &4 % //Filter length

//0igital Cutoff frequenc6 &.oDer Cutoff@ +pper Cutoff'Jc & inp t,4Enter the Digital < toff freq ency &4 %Jc2 & Jc,2

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Jc- & Jc,-T o & ,?)- (2 //Center Galuehd & +eros,-#? %J & +eros,-#? %for n & -:-- if ,n && T o7- hd,n & ,Jc2)Jc- (Kpi% else n hd,n & ,sin,Jc2C,,n)- )T o )sin,Jc-C,,n)- )T o (,,,n)- )T o CKpi % end if,abs,hd,n 9,8.8888- hd,n &8% end

endhd%


//EindoDing Fitler Coefficientsh & hd.CJ%disp,h#4@ilter indo>4xgrid,-

//%esult //!nter the 8dd Filter .ength # 11 //!nter the 0igital Cutoff frequenc6 # &Hpi/)@ "?Hpi/)'

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//Filter Coefficients are // 4( 4( 4( , 4("1


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T o & ,?)- (2 //Center Galuehd & +eros,-#? %J & +eros,-#? %for n & -:? if ,n && T o7- hd,n & -),,Jc2)Jc- (Kpi % elsehd,n &,sin,KpiC,,n)- )T o )sin,Jc2C,,n)- )T o 7sin,Jc-C,,n)- )T o (,,,n)

- )T o CKpi % end if,abs,hd,n 9,8.8888- hd,n &8% endend


//EindoDing Fitler Coefficientsh & hd.CJ%disp,h#4@ilter indo>4xgrid,-

//%esult //!nter the 8dd Filter .ength # 11 //!nter the 0igital Cutoff frequenc6 #&Hpi/"@ ?Hpi/"' //Filter Coefficients are //column 1 to >

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// 4( , 4(1"; Pass @ilter singgi=en desired freq ency response.

Program' & o, Pass ilter

//Caption: 0esign of F-% .PF Filter using Frequenc6 Sampling Techniqueclear%clc%close%? &- %

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Hr & *-#-#-#-#8.'#8#8#8/%for 5 &-:length,Hr 6,5 &,,)- ;,5)- CHr,5 %endh & +eros,-#? %! & ,?)- (2for n & -:? h- & 8% for 5 & 2:!7- h- &6,5 Ccos,,2CKpi(? C,5)- C,,n)- 7,-(2 7h-%

end h,n & ,-(? C ,6,- 72Ch- %enddisp,h#4@ilter ith? & - >ith < toff @req ency & 8.' 4xgrid,2

//%esult

//Filter Coefficients are h2n3# //column 1 to ; // // ,4(41)1 ,4(441>) " 4(4) 4(41 ") ,4(4>1") " // //column 1 // // , 4(41)1

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esult

Ex.pt.No' Design of && ilters (Butter,ort8 C *8e0$c8e+)

( ).a. Design of Digital && Butter,ort8 ilters

Aim: To design ilinear Transform method based Digital ""$ tter>orth Lo>Pass @ilter and con=erting into High Pass @ilter# and Pass @ilter and andStop @ilter sing Digital @req ency Transformation techniq e.

Program 1' && Butter,ort8 P

//Caption: To design a digital --% First 8rder IutterDorth .PF Filter //+sing Iilinear Transformationclear all%clc%

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close%s & poly,8#4s4 %

megac & 8.2CKpi% // Cutoff frequenc6H & megac(,s7 megac % //Analog first order IutterDorth filter tranfer functionT &-% //Sampling period T # 1 Second + & poly,8#4+4 %H+ & horner,H#,2(T C,,+)- (,+7- //Iilinear TransformationHJ &frmag,H+,2 #H+,3 # -2 % //Frequenc6 response for 1 pointsJ & 8:Kpi( --:Kpi%a&gca, %a.thic5ness & -%

plot,J(Kpi#HJ#4r4a.foregro nd & -%a.font0style & O%

xgrid,-xtitle,4?agnit de $esponse of Single pole LP@ @ilter < toff freq ency &8.2Cpi4#4Normali+ed Digital @req ency)))F4#4?agnit de4 %

esult

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Program !' && Butter,ort8 ;P

//Caption: To design First 8rder IutterDorth .oD Pass Filter and convert it into35


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// 9PF +sing 0igital Filter Transformationclear all%clc%close%s & poly,8#4s4 %

megac & 8.2CKpi% //Filter cutoff frequenc6H & megac(,s7 megac % //First order IutterDorth --% filter T &-% //Sampling period T # 1 Second + & poly,8#4+4 %H+0LP@ & horner,H#,2(T C,,+)- (,+7- % //Iilinear Transformationalpha & ),cos,, megac7 megac (2 (,cos,, megac) megac (2 %H 0HP@&horner,H+0LP@#),+7alpha (,-7alphaC+ //.PF to 9PF digitaltransformationHJ &frmag,H 0HP@,2 #H 0HP@,3 # -2 % //Frequenc6 response for 1 points

J & 8:Kpi( --:Kpi%a&gca, %a.thic5ness & -%

plot,J(Kpi#HJ#4r4a.foregro nd & -%a.font0style & O%xgrid,-xtitle,4?agnit de $esponse of Single pole HP@ @ilter < toff freq ency &8.2Cpi4#4Normali+ed Digital @req ency J(pi)))F4#4?agnit de4 %

esult

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Program "' && Butter,ort8 BP

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///Caption:To 0esign a 0igital --% IutterDorth .PF Filter from Analog --% //IutterDorth Filter and .PF to IPF using 0igital Transformationclear all%clc%close%omegaP & 8.2CKpi% //Filter cutoff frequenc6omegaL & ,-( CKpi% //.oDer Cutoff frequenc6 for ISFomega! & ,3( CKpi% //+pper Cutoff frequenc6 for ISF+&poly,8#4+4 %H0LP@ & ,8.2' C,-7,+;)- (,-)8. 8OC,+;)- % //Iilinear transformationalpha & ,cos,,omega!7omegaL (2 (cos,,omega!)omegaL (2 % //parameter 7alpha7

//parameter 7k7 5 & ,cos,,omega! ) omegaL (2 (sin,,omega! ) omegaL (2 Ctan,omegaP(2 %

N!? &),,+;2 ),,2CalphaC5(,57- C+ 7,,5)- (,57- %

DEN & ,-),,2CalphaC5(,57- C+ 7,,,5)- (,57- C,+;2 %H 0 P@&horner,H0LP@#N!?(DEN % //.PF to IPF conversion using digitaltransformationdisp,H 0 P@#4Digital P@ ""$ @ilter H, & 4 %HJ &frmag,H 0 P@,2 #H 0 P@,3 # -2 % //frequenc6 responseJ & 8:Kpi( --:Kpi%a&gca, %a.thic5ness & -%

plot,J(Kpi#HJ#4r4a.foregro nd & -%a.font0style & O%xgrid,-xtitle,4?agnit de $esponse of P@ @ilter c toff freq ency *8.2#8. /4#4Normali+edDigital @req ency)))F4#4?agnit de4 %

esult

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Program #' && Butter,ort8 BS

//Caption:To 0esign a 0igital --% IutterDorth .PF Filter from Analog --%39


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//IutterDorth Filter and .PF to ISF using 0igital Transformationclear all%clc%close%omegaP & 8.2CKpi% //Filter cutoff frequenc6omegaL & ,-( CKpi% //.oDer Cutoff frequenc6 for ISFomega! & ,3( CKpi% //+pper Cutoff frequenc6 for ISF+&poly,8#4+4 %H0LP@ & ,8.2' C,-7,+;)- (,-)8. 8OC,+;)- //Iilinear transformationalpha & ,cos,,omega!7omegaL (2 (cos,,omega!)omegaL (2 % //parameter7alpha7 5 & tan,,omega! ) omegaL (2 Ctan,omegaP(2 % //parameter 7k7

N!? &,,+;2 ),,2Calpha(,-75 C+ 7,,-)5 (,-75 % // umerator DEN & ,-),,2Calpha(,-75 C+ 7,,,-)5 (,-75 C,+;2 % //0enominator

H 0 S@&horner,H0LP@#N!?(DEN % //.PF to ISF conversion using digitaltransformationHJ &frmag,H 0 S@,2 #H 0 S@,3 # -2 % //frequenc6 response for 1 pointsJ & 8:Kpi( --:Kpi%a&gca, %a.thic5ness & -%

plot,J(Kpi#HJ#4r4a.foregro nd & -%a.font0style & O%xgrid,-xtitle,4?agnit de $esponse of S@ @ilter c toff freq *8.2#8. / 4#4Normali+ed Digital@req ency)))F4#4?agnit de4 %

esult

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( ).0. Design of Digital && *8e0$s8e+ ilter

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Aim: To design ilinear Transform method based Digital ""$ Pass @ilter.

Program' && *8e0$s8e+ P

//Program To 0esign the 0igital CheJ6shev --% Filter

clear%clc%close%Jp & inp t,4Enter the Digital Pass and Edge @req ency4 %Js & inp t,4Enter the Digital Stop and Edge @req ency4 %T & inp t,4Sampling "nter=al4

megaP & ,2(T Ctan,Jp(2megaS & ,2(T Ctan,Js(2

Delta- & inp t,4Enter the Pass and $ipple4 %Delta2 & inp t,4Enter the Stop and $ipple4 %Delta & sqrt,,,-(Delta2 ;2 )-Epsilon & sqrt,,,-(Delta- ;2 )-

N & ,acosh,Delta(Epsilon (,acosh, megaS( megaP N & ceil,N

mega< & megaP(,,,,-(Delta- ;2 )- ;,-(,2CN*pols#gn/ & +pch-,N#Epsilon# megaP

Hs & poly,gn#4s4#4coeff4 (real,poly,pols#4s4+ & poly,8#4+4 %H+ & horner,Hs#,,2(T C,,+)- (,+7-HJ &frmag,H+,2 #H+,3 # -2 % //Frequenc6 response for 1 pointsJ & 8:Kpi( --:Kpi%a&gca, %a.thic5ness & -%

plot,J(Kpi#abs,HJ #4r4a.foregro nd & -%a.font0style & O%xgrid,-xtitle,4?agnit de $esponse of


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//Sampling -nterval 1 // T # // 1( // 8megaP # // 4(*)> // !psilon # // 4(; // #

// 1( 4;> )< // # // ( // 8megaC # // 4(; 4"*>> // gn # // 4( < 5 4( "4 >1*i , 4( * > < , 4( "4 >1*i // 9s # // // 4( 1*s 5 s // //9$ # // // 4( 4; *1 , ;( >*1 *$ //,,B4( ?4( * > // ans # // 4(


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// 9$ # // // // 4(4 44 * // 9$ # // // 4(4 44< , 1(");


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Program' Decimation 0$ Pol$p8ase Decomposition

//Caption:0ecimation J6 @ Filter .ength # "4

//Cutoff Frequenc6 Ec # Hpi/ //Pass Jand !dge frequenc6 fp # 4( and a Stop Jand edge frequenc6 fs # 4("1 // Choose the numJer of cosine functions and create a dense grid // in &4@4( ' and &4("1@4( ' //magnitude for pass Jand # 1 K stop Jand # 4 2i(e3 &1 4' //Eeighting function #& 1'clear%clc%close%? & 38% //Filter .engthD & 2% //0ecimation Factor # Jc & Kpi(2% //Cutoff Frequenc6Jp & Jc(,2CKpi % //PassJand !dge Frequenc6Js & 8.3-% //StopJand !dge Frequenc6hn&eqfir,?#*8 Jp%Js . /#*- 8/#*2 -/ %disp,hn#4The LP@ @ilter >1

//column < to 1) //4(4 1"


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//4()> );* 4()> );* 4(4>1 , 4(4")>>1 , 4(44)*;*1 ,4(44 < ")

//column 1 //, 4(41


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Program' Scila0 program for Perio ogram 0ase Spectrum Estimation

//Caption: Periodogram !stimate of Liven 0iscrete Sequence

//x2n3 # 1@4@ @4@"@1@4@ N //using 0FT clear%clc%close%

N &M% // " 5 4(1 1" 4"i // ( 5 i // , (;4;14*< 5 )(1 1" 4"i // "( , "(*;)0,1*i // , (;4;14*< , )(1 1" 4"i // ( , i // , 1( > " , 4(1 1" 4"i //

// Peridogram of x2n3 is Pxx2k/ 3# //

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// 14(1 // 4( 14; 1"* // 1(1 // "(4"> 1"* // 4(* // 4( 14;


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5rc8itecture of t8e Digital Signal Processor

ne of the biggest bottlenec5s in exec ting DSP algorithms is transferringinformation to and from memory. This incl des data# s ch as samples from theinp t signal and the filter coefficients# as >ell as program instr ctions# the binarycodes that go into the program seq encer. @or example# s ppose >e need to

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m ltiply t>o n mbers that reside some>here in memory. To do this# >e m st fetchthree binary =al es from memory# the n mbers to be m ltiplied# pl s the programinstr ction describing >hat to do.

@ig re ,a sho>s ho> this seemingly simple tas5 is done in a traditionalmicroprocessor. This is often called a Qon Ne mann architect re# after the brilliantAmerican mathematician Rohn Qon Ne mann ,-O83)-O . Qon Ne mann g idedthe mathematics of many important disco=eries of the early t>entieth cent ry. Hismany achie=ements incl de: de=eloping the concept of a stored program comp ter#formali+ing the mathematics of q ant m mechanics# and >or5 on the atomic

bomb.

As sho>n in ,a # a Qon Ne mann architect re contains a single memory and asingle b s for transferring data into and o t of the central processing nit ,o n mbers req ires at least three cloc5 cycles# one to transfer eachof the three n mbers o=er the b s from the memory to the e ass me that it remains inthe hen =ery fast processing isreq ired# and >e are >illing to pay the price of increased complexity.

This leads s to the Har=ard architect re# sho>n in ,b . This is named for the >or5done at Har=ard !ni=ersity in the -O'8s nder the leadership of Ho>ard Ai5en,-O88)-O 3 . As sho>n in this ill stration# Ai5en insisted on separate memories fordata and program instr ctions# >ith separate b ses for each. Since the b sesoperate independently# program instr ctions and data can be fetched at the sametime# impro=ing the speed o=er the single b s design. ?ost present day DSPs sethis d al b s architect re.

@ig re ,c ill strates the next le=el of sophistication# the S per Har=ardArchitect re. This term >as coined by Analog De=ices to describe the internal

operation of their ADSP)2-8 x and ne> ADSP)2--xx families of Digital SignalProcessors. These are called SHA$< DSPs# a contraction of the longer term#S per Har=ard A$ays# t>o areas are important eno gh to be incl ded in @ig. c: aninstr ction cache# and an "( controller.

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@irst# let4s loo5 at ho> the instr ction cache impro=es the performance of theHar=ard architect re. A handicap of the basic Har=ard design is that the datamemory b s is b sier than the program memory b s. Jhen t>o n mbers arem ltiplied# t>o binary =al es ,the n mbers m st be passed o=er the data memory

b s# >hile only one binary =al e ,the program instr ction is passed o=er the program memory b s. To impro=e pon this sit ation# >e start by relocating partof the 1data1 to program memory. @or instance# >e might place the filtercoefficients in program memory# >hile 5eeping the inp t signal in data memory.,This relocated data is called 1secondary data1 in the ill stration . At first glance#this doesn4t seem to help the sit ation% no> >e m st transfer one =al e o=er thedata memory b s ,the inp t signal sample # b t t>o =al es o=er the programmemory b s ,the program instr ction and the coefficient . "n fact# if >e >ereexec ting random instr ctions# this sit ation >o ld be no better at all.

Ho>e=er# DSP algorithms generally spend most of their exec tion time in loops.This means that the same set of program instr ctions >ill contin ally pass from

program memory to the ith the coefficientsthat m st also be fetched along this path. Ho>e=er# on additional exec tions of theloop# the program instr ctions can be p lled from the instr ction cache. Thismeans that all of the memory to


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dsp laboratory experiments

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