DSP Lab Manual Print Edition

8/3/2019 DSP Lab Manual Print Edition

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Digital Signal

Processing

Lab Manual

DSPDigital Signal Processing Laboratory Manual for Under-Graduatecourse in Electronics and Communication. Bharath P


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Contents

1. Sampling Theorem2. Impulse Response3. Linear Convolution4. Circular Convolution5. Auto correlation & its properties6. Cross correlation & its properties7. Difference Equation8. N-Point DFT9. Linear Convolution using DFT & IDFT10. Circular Convolution using DFT & IDFT11. FIR Filters12.a. IIR Filters - Butterworth

b. IIR Filters - Chebyshev Type I

1. Linear Convolution2. Circular Convolution3. N-Point DFT


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Prerequisites:

As an exercise, it is recommended to go through the basics of Signals & Sytems,Digital Signal Processing and some details about DSP hardware & processors.

References:

[1] Oppenheim & Schaffer: Digital Signal Processing, Prentice-Hall.[2] B P Lathi: Modern Digital and Analog communication systems, Oxford.[3] Rulph Chassaing: Digital Signal Processing and Applications with the C6713 and

C6416 DSK,John Wiley.[4] Avatar Singh & S Srinivasan: Digital Signal Processing, Thomson Learning.

[5] TMS320C6713 DSK- Technical Reference, Spectrum Digital, Inc.[6]TMS320C6000 Code Composer Studio Tutorial (Literature Number: SPRU301C),Texas Instruments.

[7] Getting Started with Matlab, MATLAB.


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Matlab Programs


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1.Sampling Theoremclear all;

close all;

clc;

tf=0.05;

t=0:0.00005:tf;

f=input('Enter the analog frequency,f = ');

xt=cos(2*pi*f*t);

fs1=1.3*f;

n1=0:1/fs1:tf;

xn=cos(2*pi*f*n1);

subplot(311);

plot(t,xt,'b',n1,xn,'r*-');title('Undersampling plot');

xlabel('time');

ylabel('Amplitude');

fs2=2*f;

n2=0:1/fs2:tf;

xn=cos(2*pi*f*n2);

subplot(312);

plot(t,xt,'b',n2,xn,'r*-');

title('Nyquist plot');

xlabel('time');


fs3=6*f;

n3=0:1/fs3:tf;

xn=cos(2*pi*f*n3);

subplot(313);

plot(t,xt,'b',n3,xn,'r*-');

title('Oversampling plot');

xlabel('time');



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Output

Enter the analog frequency,f = 200


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2.Impulse Responseclear all;

close all;

clc;

disp('Difference Equation of a digital system');

N=input('Desired Impulse response length = ');

b=input('Coefficients of x[n] terms = ');

a=input('Coefficients of y[n] terms = ');

h=impz(b,a,N);

disp('Impulse response of the system is h = ');

disp(h);

n=0:1:N-1;

figure(1);

stem(n,h);

xlabel('time index');

ylabel('h[n]');

title('Impulse response');

figure(2);

zplane(b,a);

xlabel('Real part');

ylabel('Imaginary part');

title('Poles and Zeros of H[z] in Z-plane');


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Output[Given y(n)-y(n-1)+0.9y(n-2)= x(n)]

Difference Equation of a digital system

Desired Impulse response length = 100Coefficients of x[n] terms = 1

Coefficients of y[n] terms = [1 -1 0.9]


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3.Linear Convolutionclear all;

close all;

clc;

x=input('x[n]= ');

l=length(x);

h=input('h[n]=');

m=length(h);

num=(l+m)-1;

x_pad=[x,zeros(1,num-l)];

h_pad=[h,zeros(1,num-m)];

new_matrix=zeros(num,num);

new_mat(:,1)=x_pad';

for j=2:num new_mat(1,j)=new_mat(num,j-1);for i=2:num

new_mat(i,j)=new_mat(i-1,j-1);

end

end

result=new_mat*h_pad';

disp('y[n]= ');

disp(result');

low=min([result',x,h])-5;

high=max([result',x,h])+5;

subplot(1,3,1);

stem(x);xlabel('n');

ylabel('x[n]');

axis([1 num low high]);

subplot(1,3,2);

stem(h);

xlabel('n');

ylabel('h[n]');


subplot(1,3,3);

stem(result');

xlabel('n');

ylabel('y[n]');



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Output

x[n]= [1 2 3 4]

h[n]=[2 1]

y[n]=2 5 8 11 4


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4.Circular Convolutionclear all;

close all;

clc;

x=input('x[n]= ');

h=input('h[n]= ');

num=input('Enter the length of the sequences = ');

new_matrix=zeros(num,num);

new_mat(:,1)=x';

for

j=2:num new_mat(1,j)=new_mat(num,j-1);

for i=2:num

new_mat(i,j)=new_mat(i-1,j-1);

endend

result=new_mat*h';

disp('y[n]= ');

disp(result');

low=min([result',x,h])-5;

high=max([result',x,h])+5;

subplot(1,3,1);

stem(x);

xlabel('n');

ylabel('x[n]');

axis([1 num low high]);subplot(1,3,2);

stem(h);

xlabel('n');

ylabel('h[n]');


subplot(1,3,3);

stem(result');

xlabel('n');

ylabel('y[n]');



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Output

x[n]= [1 2 3 4]

h[n]= [2 1 2 1]Enter the length of the sequences = 4

y[n]=

14 16 14 16


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5.Auto-correlation & its propertiesclear all;

close all;

clc;

x_n=input('x[n]= ');

L=length(x_n);

x_minus_n=fliplr(x_n);

Rxx=conv(x_n,x_minus_n);

disp('Verification of property 1');

if(Rxx==fliplr(Rxx))

disp('Rxx[n] and Rxx[-n] are identical');

disp('Hence Auto correlation has even symmetry');

elsedisp('Rxx[n] and Rxx[-n] are not identical');

end


[max_val index]=max(Rxx);

if(index==L)

disp('maximum is at the origin');

else

disp('maximum is not at the origin');

end


energy=sum(x_n.^2);max_Rxx=max(Rxx);

disp('Energy of x[n] = ');

disp(energy);

disp('Maximun of Rxx[n] = ');

disp(max_Rxx);

disp('Hence maximum of Rxx is equal to Energy of x[n]');

N=length(Rxx);

X_k=fft(x_n,N);

EDS=abs(X_k).^2;

Rxx_k=fft(Rxx,N);

t=-(L-1):(L-1);

subplot(2,2,1);stem(t,[zeros(1,L-1),x_n]);

xlabel('n');

ylabel('x[n]');

subplot(2,2,2);

stem(t,Rxx);

xlabel('n');

ylabel('Rxx[n]');

title('Autocorrelation');

subplot(2,2,3);

stem(EDS);

xlabel('n');

ylabel('EDS');

title('Enegry density of x[n]');


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subplot(2,2,4);

stem(abs(Rxx_k));

xlabel('k');ylabel('Rxx[k]');

title('DFT of Rxx[n]');


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Output

x[n]= [1 2 3 4]

Verification of property 1Rxx[n] and Rxx[-n] are identical

Hence Auto correlation has even symmetry

Verification of property 2

maximum is at the origin


Energy of x[n] =

30

Maximun of Rxx[n] =

30

Hence maximum of Rxx is equal to Energy of x[n]


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6.Cross-correlation & its propertiesclear all;

close all;

clc;

x_n=input('x[n]= ');

N=length(x_n);

y_n=input('y[n]= ');

M=length(y_n);

y_minus_n=fliplr(y_n);

x_minus_n=fliplr(x_n);

Rxy=conv(x_n,y_minus_n);

t=-(N-1):(M-1);

t2=-(M-1):(N-1);

disp('Verification of property 1');disp('Rxy[n]and Ryx[n] ');

Ryx=conv(x_minus_n,y_n);

if(Rxy==Ryx)

disp('are not commutative');

else

disp('are commutative');

end


disp('Rxy[n]and Ryx[-n] ');

if(Rxy==fliplr(Ryx))

disp('are equal');

elsedisp('are not equal');

end


disp('The sequences ');

if(Rxy(M+1)==0)

disp('are orthogonal');

else

disp('are not orthogonal');

end

disp('DFT Rxy[n]=X[k].Y[k]');

temp=fft(Rxy);Rxy_k=abs(temp);

X_k=fft(x_n,length(Rxy));

Y_k=fft(y_n,length(Rxy));

temp2=(X_k).*conj(Y_k);

temp3=abs(temp2);

subplot(3,2,1);

stem(t,[zeros(1,M-1),x_n]);

xlabel('n'); ylabel('x[n]');

subplot(3,2,2);

stem(t,[y_minus_n,zeros(1,N-1)]);

xlabel('n');

ylabel('y[-n]');


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subplot(3,2,3)stem(t,Rxy);

xlabel('n');

ylabel('Rxy[n]');

title('Crosscorrelation');subplot(3,2,4);

stem(t2,Ryx);

xlabel('n');

ylabel('Ryx[n]');

title('Crosscorrelation');

subplot(3,2,5);

stem(Rxy_k);

xlabel('k');

ylabel('Rxy[k]');

title('DFT of Rxy[n]');

subplot(3,2,6);

stem(temp3);

xlabel('k');

ylabel('X[k].Y[k]');

title('DFT x[n].DFT y[n]');


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Output

x[n]= [1 2 3 4]

y[n]= [4 3 2 1]


Rxy[n]and Ryx[n]

are commutative


Rxy[n]and Ryx[-n]

are equal


The sequences are not orthogonal

DFT Rxy[n]=X[k].Y[k]


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7.Difference Equationclear all;

close all;

clc;

disp('Enter the parameters of Difference Equation of a digital system');

b=input('Coefficients of x[n] terms = ');

a=input('Coefficients of y[n] terms = ');

xn=input('Enter the input exitation x[n] = '); %of length 1 to 100

yi=input('Enter the initial conditions of y = '); %if necessary

%xi=('Enter the initial conditions of x = ');

%yi of length 1 to (a-1)

%xi of length 1 to (b-1)

initialc=filtic(b,a,yi);

%initialc=filtic(b,a,yi,xi);y_complete=filter(b,a,xn,initialc);

y_forced=filter(b,a,xn);

y_natural=y_complete-y_forced;

subplot(3,1,1);

stem(y_natural);

title('Natural response of the system');

subplot(3,1,2);

stem(y_forced);

title('Forced response of the system');

subplot(3,1,3);

stem(y_complete);

title('Complete response of the system');


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Output

Enter the parameters of Difference Equation of a digital system

Coefficients of x[n] terms = 1Coefficients of y[n] terms = [1 -1 0.9]

Enter the input exitation x[n] = [1 zeros(1,99)]

Enter the initial conditions of y = [-1 0 0]


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8.N-point DFTclear all;

close all;

clc;

x=input('Enter the sequence x[n]= ');

N=input('Enter the value N point= ');

L=length(x);

x_n=[x,zeros(1,N-L)];

for i=1:N

for j=1:N

temp=-2*pi*(i-1)*(j-1)/N;

DFT_mat(i,j)=exp(complex(0,temp));

endend

X_k=DFT_mat*x_n';

disp('N point DFT is X[k] = ');

disp(X_k);

mag=abs(X_k);

phase=angle(X_k)*180/pi;

subplot(2,1,1);

stem(mag);

xlabel('frequency index k');

ylabel('Magnitude of X[k]');

axis([0 N+1 -2 max(mag)+2]);

subplot(2,1,2);

stem(phase);

xlabel('frequency index k');

ylabel('Phase of X[k]');

axis([0 N+1 -180 180]);


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Output

Enter the sequence x[n]= [1 2 3 4]

Enter the value N point= 4N point DFT is X[k] =

10.0000

-2.0000 + 2.0000i

-2.0000 - 0.0000i

-2.0000 - 2.0000i


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9. Linear Convolution using DFT & IDFTclear all;

close all;

clc;

x=input('x[n]= ');

l=length(x);

h=input('h[n]= ');

m=length(h);

num=(l+m)-1;

XN=fft(x,num);

HN=fft(h,num);

YN=XN.*HN;y=ifft(YN,num);

disp('y[n]= ');

disp(y);

low=min([y,x,h])-5;

high=max([y,x,h])+5;

subplot(1,3,1);

stem(x);

xlabel('n');

ylabel('x[n]');


subplot(1,3,2);

stem(h);

xlabel('n');

ylabel('h[n]');


subplot(1,3,3);

stem(y);

xlabel('n');

ylabel('y[n]');



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Output

x[n]= [1 2 3 4]

h[n]= [2 1]y[n]=

2 5 8 11 4


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10. Circular Convolution using DFT & IDFTclear all;

close all;

clc;

disp('Enter the sequences of equal lengths');

x=input('x[n]= ');

N=length(x);

h=input('h[n]= ');

XN=fft(x,N);

HN=fft(h,N);

YN=XN.*HN;

y=ifft(YN,N);

disp('y[n]= ');

disp(y);

low=min([y,x,h])-5;

high=max([y,x,h])+5;

subplot(1,3,1);

stem(x);

xlabel('n');

ylabel('x[n]');

axis([1 N low high]);

subplot(1,3,2);

stem(h);

xlabel('n');

ylabel('h[n]');


subplot(1,3,3);

stem(y);

xlabel('n');

ylabel('y[n]');



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Output

Enter the sequences of equal lengths

x[n]= [1 2 3 4]h[n]= [2 1 2 1]

y[n]=

14 16 14 16


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11. FIR Filtersclear all;

close all;

clc;

wn=input('Enter the passband frequency between 0 & 1 (normalised) = ');

%wn=[w1 w2];

%wn is a vector,for Bandpass & Bandstop

n=input('Enter the order of the filter = ');

%beta=input('Enter the value of beta');

%beta for Kaiser only

b=fir1(n,wn,hamming(n+1)); %replace by following for other windows

%blackman(n);

%hanning(n);%hann(n);

%barlett(n);

%boxcar(n);

%kaiser(n,beta);

%b=fir1(n,wn,'high',XXXXXXX(n)); Highpass window

%b=fir1(n,wn,XXXXXXX(n)); Bandpass window

%b=fir1(n,wn,'stop',XXXXXXX(n)); Bandstop window

[h,w]=freqz(b,1,512);

dB=20*log10(abs(h));

figure(1);

subplot(2,1,1);

plot(w/pi,dB);

title('Magnitude response');

xlabel('Normalised frequency');

ylabel('Magnitude in dB');

grid;

subplot(2,1,2);

plot(w/pi,angle(h));

title('Phase response');


ylabel('Phase in degrees');

grid;

figure(2);

stem(impz(b,1));

title('Impulse response');

xlabel('Time index n');



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Output

Enter the passband frequency between 0 & 1 (normalised) = 0.3

Enter the order of the filter = 20


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12.a IIR Filters - Butterworth

clear all;

close all;

clc;

wp=input('Enter the passband edge Normalised frequency = ');

%wp=wn, for 3dB cutoff frequency

ws=input('Enter the stopband edge Normalised frequency = ');

%wp=[w1 w2]; ws=[w3 w4];

%wp & ws are vectors, for Bandpass & Bandstop

Dp=input('Enter the passband attenuation level (dB) = ');

Ds=input('Enter the stopband attenuation level (dB) = ');

%N=input('Enter the order of the filter = ');

%order=N/2, for Bandpass & Bandstop

[N,wn]=buttord(wp,ws,Dp,Ds); %skip if N & 3dB cutoff frequency is known

[b,a]=butter(N,wn); %replace by following for other filters

%[b,a]=butter(N,wn,'high'); Highpass filter

%[b,a]=butter(N,wn); Bandpass filter

%[b,a]=butter(N,wn,'stop'); Bandstop filter

[h,w]=freqz(b,a);

mag=20*log10(abs(h));

phase=180*angle(h)/pi;

figure(1);

plot(w,abs(h));

title('Butterworth Lowpass Filter');


ylabel('Magnitude');

grid;

figure(2);

subplot(2,1,1);

plot(w,mag);




grid; subplot(2,1,2);

plot(w,phase);




grid;


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Output

Enter the passband edge Normalised frequency = 0.3

Enter the stopband edge Normalised frequency = 0.6Enter the passband attenuation level (dB) = 3

Enter the stopband attenuation level (dB) = 40


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12.b IIR Filters - Chebyshev

clear all;

close all;

clc;

wp=input('Enter the passband edge Normalised frequency = ');

%wp=wn, for 3dB cutoff frequency

ws=input('Enter the stopband edge Normalised frequency = ');

%wp=[w1 w2]; ws=[w3 w4];

%wp & ws are vectors, for Bandpass & Bandstop

Rp=input('Enter the passband attenuation level (dB) = ');

Rs=input('Enter the stopband attenuation level (dB) = ');

%N=input('Enter the order of the filter = ');

%order=N/2, for Bandpass & Bandstop[N,wn]=cheb1ord(wp,ws,Rp,Rs);

%skip if order and 3dB cutoff frequency is known

[b,a]=cheby1(N,Rp,wn); %replace by following for other filters

%[b,a]=cheby1(N,Rp,wn,'high'); Highpass filter

%[b,a]=cheby1(N,Rp,wn); Bandpass filter

%[b,a]=cheby1(N,Rp,wn,'stop'); Bandstop filter

[h,w]=freqz(b,a);

mag=20*log10(abs(h));

phase=180*angle(h)/pi;

figure(1);

plot(w,abs(h));

title('Chebyshev Lowpass Filter');


ylabel('Magnitude');

grid;

figure(2);

subplot(2,1,1);

plot(w,mag);




grid;

subplot(2,1,2);

plot(w,phase);




grid;


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Output

Enter the passband edge Normalised frequency = 0.3

Enter the stopband edge Normalised frequency = 0.6

Enter the passband attenuation level (dB) = 3

Enter the stopband attenuation level (dB) = 40


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C Programs


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1. Linear Convolution#include

#include

int m,n,i,j,x[30],y[30],h[30];

void main()

{

printf("Enter the length of x\n");

scanf("%d",&m);

printf("Enter the length of h\n");

scanf("%d",&n);

printf("Enter x\n");

for(i=0;i


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2. Circular Convolution#include

#include

int m,n,i,j,k,x[30],y[30],h[30],a[30],b[30];

void main()

{

printf("Enter the length of x\n");

scanf("%d",&m);


for(i=0;i


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Output

Enter the length of x

4Enter x

1

2

3

4

Enter h

2

1

2

1

Circular convolution, y is 14 16 14 16


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3. N-Point DFT#include

#include

void main()

{

int i,j,n;

short N;

short x[10];

float pi=3.1416;

float sumRe,sumIm;

float cosine=0,sine=0;

float out_real[10]={0.0},out_image[10]=(0.0);

printf("Enter the length of the sequence\n");

scanf("%d",&n);

printf("Enter N\n");

scanf("%d",&N);


for(i=n+1;in)for(i=n;i


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Output

Enter the length of the sequence

4Enter N

4

Enter x

1

2

3

4

N point DFT is

10.0 +j(0.0)

-2.0 +j(-2.0)

-2.0 +j(-0.0)

-2.0 +j(2.0)


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Text Key Steps

Text Commands for plotting a figure

Text Comments


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