dsp manual

2011

By- Ashutosh

www.citystudentsgroup.blogspot.com

1/5/2011

DSP LAB PROGRAM MANUAL


©Brought to you by www.citystudentsgroup.blogspot.com

CONTENTS 1. SAMPLING THEOREM………………………………………………………..1-3

2. IMPULSE RESPONSE………………………………………………………….3-4

3. LINEAR CONVOLUTION……………………………………………………..4-8

4. CIRCULAR CONVOLUTION OF TWO GIVEN SEQUENCE……………..8-9

5. N-POINT DFT…………………………………………………………………...9-10

6. LINEAR CONVOLUTION USING DFT&IDFT……………………………..11-11

7. CIRCULAR CONVOLUTION USING DFT&IDFT…………………………12-12

8. AUTOCORRELATION………………………………………………………...12-16

9. CROSSCORRELATION……………………………………………………….16-19

10. FIR FILTER……………………………………………………………………..19-23

11. IIR FILTER DESIGN…………………………………………………………...23-26

12. SOLVING A DIFFERENCE EQUATION…………………………………….27-30

CCS PROGRAMMING

1. LINEAR CONVOLUTION………………………………………………………31-31

2. CIRCULAR CONVOLUTION…………………………………………………..31-32

3. COMPUTATION OF N-POINT DFT…………………………………………...32-32

4. IMPULSE RESPOSE OF THE DIFFERENT ORDER SYSTEM…………….32-33



1.VERIFICATION OF SAMPLING THEOREM:

tfinal=0.05; t=0:0.00005:0.05; fd=input(‘enter analog frequency'); xt=sin(2*pi*fd*t); subplot(3,3,1); plot(t,xt); fs1=1.3*fd; n1=0:1/fs1:tfinal; xn=sin(2*pi*n1*fd); subplot(3,3,1); plot(t,xt,'b',n1,xn,'r*-'); title('undersampling plot'); fs2=2*fd; n2=0:1/fs2:tfinal; xn=sin(2*pi*fd*n2); subplot(3,3,2); plot(t,xt,'b',n2,xn,'r*-'); title('nyquist plot'); fs3=5*fd; n3=0:1/fs3:tfinal; xn=siin(2*pi*fd*n3); subplot(3,3,3); plot(t,xt,'b',n3,xn,'r*-'); title('oversampling plot'); xlabel('time'); ylabel('amplitude'); legend('analog','discrete');

Result:

enter analog frequency 200



2.IMPULSE RESPONSE OF A GIVEN SYSTEM:

y=input('the output sequence y(n) of the system ='); x=input('the input sequence of the sysytem ='); h=deconv(y,x); disp('the impulse response of the system is ='); disp(h); N=length(h); n=0:1:N-1; stem(n,h); xlabel('time index n'); ylabel('amplitude'); title('impulse response of a sysytem'); yv= conv(x,h); disp('the verified output sequence is'); disp(yv);

RESULT:

the output sequence y(n) of the system =[1 2 1 1 0 -1]

the input sequence of the sysytem =[1 1 1 1]

the impulse response of the system is =

1 1 -1

the verified output sequence is

1 2 1 1 0 -1

GRAPH:

3.LINEAR CONVOLUTION OF TWO GIVEN SEQUENCE:

LEVEL-1: RIGHT SIDED

x1=input('enter first sequence'); x2=input('enter second sequence'); y=conv(x1,x2);



disp('linear convolution of x1&x2 is y='); disp(y); subplot(2,2,1); stem(y); xlabel('time index n'); ylabel('amplitude'); title('convolution output'); subplot(2,2,2); stem(x1); xlabel('time index n'); ylabel('amplitude'); title('plot of x1'); subplot(2,2,3); stem(x2); xlabel('time index n'); ylabel('amplitude'); title('plot of x2');

RESULT:

enter first sequence [1 2 3 4]

enter second sequence [2 3 2 4]

linear convolution of x1&x2 is y=

2 7 14 25 26 20 16

GRAPH:



LEVEL-2: TWO SIDED SEQUENCE x1=[1 2 3 2 1 3 4]; n1=-3:3; x2=[2 -3 4 -1 0 1]; n2=-1:4; ybegin=n1(1)+n2(1); yend=n1(length (x1))+ n2(length(x2)); ny=[ybegin:yend]; y=conv(x1,x2); disp('linear convolution of x1&x2 is y='); disp(y); subplot(2,2,1); stem(ny,y); xlabel('time index n'); ylabel('amplitude'); title('convolution output'); subplot(2,2,2); stem(n1,x1); xlabel('time index n'); ylabel('amplitude'); title('plot of x1'); subplot(2,2,3); stem(n2,x2); xlabel('time index n'); ylabel('amplitude'); title('plot of x2');

RESULT:

linear convolution of x1&x2 is y=

2 1 4 2 6 9 3 2 15 -3 3 4

GRAPH:



4. CIRCULAR CONVOLUTION OF TWO GIVEN SEQUENCE:

x=[1 2 3 4];

h=[1 2 3 4]; N= max(length(x),length(h)); for n=0:N-1

y(n+1)=0; for k=0:N-1

i=mod((n-k),N); if i<0 i=i+N;

end y(n+1)=y(n+1)+(h(k+1)*x(i+1));

end end disp('circular convolution of x1&x2 is y=');

disp(y); n1=0:N-1;

title('circular convolution output y(n)');

5.COMPUTATION OF N-POINT DFT OF A GIVEN SEQUENCE AND TO PLOT

MAGNITUDE AND PHASE SPECTRUM:

x=[1 2 3 6]; N=4; xk=fft(x,N); n=0:1:N-1; figure(1); stem(n,abs(xk)); xlabel('k'); ylabel('|x(k)|'); title('magnitude spectrum'); figure(2); stem(n,angle(xk)); xlabel('k'); ylabel('angle(xk)'); title('phase spectrum'); figure(3); n1=0:1:length(x)-1; stem(n1,x); xlabel('n'); ylabel('x[n]'); title('original signal');

GRAPHS:

DSP LAB


6.LINEAR CONVOLUTION OF TWO GIVEN SEQUENCES USING

LINEAR CONVOLUTION:

x1=[1 2 3 4]; x2=[1 2 3 4]; N=length(x1)+length(x2)-1; X1=fft(x1,N); X2=fft(x2,N); y=X1.*X2; yn=ifft(y,N); disp('linear convolution of x1 & x2 is yn='disp('yn'); disp('output using convolution'yv=conv(x1,x2); disp(yv); stem(yn); title('linear convolution output y(n)'

RESULT:

linear convolution of x1 & x2 is yn=

yn

output using convolution

1 4 10 20 25 24 16


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LINEAR CONVOLUTION OF TWO GIVEN SEQUENCES USING DFT

'linear convolution of x1 & x2 is yn=');

'output using convolution');

'linear convolution output y(n)');

linear convolution of x1 & x2 is yn=

1 4 10 20 25 24 16

DFT AND IDFT:



GRAPH:

7.CIRCULAR CONVOLUTION OF TWO GIVEN SEQUENCES USING DFT AND

IDFT:

x1=[1 2 3 4]; x2=[1 2 3 4]; N=max(length(x1),length(x2)); X1=fft(x1,N); X2=fft(x2,N); y=X1.*X2; yn=ifft(y,N); disp('linear convolution of x1 & x2 is yn='); disp('yn'); stem(yn); title('linear convolution output y(n)');

RESULT:

Circular convolution of x1 & x2 is yn=

26 28 26 20

GRAPHS:



8.GENERATION OF AUTOCORRELATION SEQUENCE:

X=[3 -1 2 1]; Y=Xcorr(X); Y=conv(x,fliplr(X)); disp('autocorrelated sequence'); disp('y'); figure(1); stem(y); title('generation of autocorrelation sequence');



n=∞

∞

8.1-For ENERGY Signal:

Properties of Autocorrelation:

1. Autocorrelation is an even function. 2. At zero lag at l=0, the sample value of the autocorrelation sequence

has its maximum value which is equal to energy of the signal.

Yxx[0]= Σx = Σx2[n]

3. The autocorrelation sequence of noise corrupted signal is also periodic in nature.

MATLAB IMPLEMENTATION:

n=-5:5; N=10; x1=ones(1,11); Y=xcorr(x1); disp('autocorrelated sequence'); disp('y'); figure(2); subplot(2,1,1); stem(n,x1); title('square sequence'); subplot(2,1,2); k=-N:N; stem(k,Y); title('autocorrelated output'); xlabel('lag index');



ylabel('lag index');

8.2-Autocorrelation for Second sequence:

N=30; n=1:N; x=cos(pi*0.25*n); d=rand(1,N)-0.5; y=x+d; r=conv(y,fliplr(y)); [ry,lag]=xcorr(y); [rn,lag1]=xcorr(d); figure(1); subplot(3,1,1); stem(x); title('reference sinusoidal sequence'); subplot(3,1,2); stem(y); title('noise corrupted signal'); subplot(3,1,3); stem(lag,r); title('autocorrelation seq of corrupted signal'); xlabel('lag index'); ylabel('amplitude');



figure(2); stem(lag1,rn); title('autocorrelation seq of noise'); xlabel('lag index'); ylabel('amplitude');

GRAPHS:



9.CROSSCORRELATION: x=input('type in the reference sequence ='); y=input('type in the second seq='); n1=length(y)-1; n2=length(x)-1; r=conv(x,fliplr(y)); disp('crosscorrelation output is='); disp(r); k=(-n1):n2; stem(k,r); xlabel('lag index'); ylabel('amplitude');

RESULT:

type in the reference sequence =[1 3 -2 1 2 -1 4 4 2]

type in the second seq=[2 -1 4 1 -2 3]

crosscorrelation output is=

3 7 -11 14 13 -15 28 6 -2 21 12 12 6 4

GRAPH:



Properties-1 ( ryx(l) = rxy(l)) xr=[1 2 3 -1]; x2=[3 -1 1 2]; [r1,l1]=xcorr(xr,x2); stem(l1,r1); disp(r1); [r2,l2]=xcorr(x2,xr); stem(l2,r2); disp(r2);

RESULT:

2.0000 5.0000 7.0000 2.0000 2.0000 10.0000 -3.0000

-3.0000 10.0000 2.0000 2.0000 7.0000 5.0000 2.0000

GRAPH:



Properties-2:

x1=[1 2 3 -2 0 0]; x2=[0 0 1 2 3 -1]; y=xcorr(x1,x2); disp(y); subplot(1,1,1); stem(y);

RESULT:

-1.0000 1.0000 5.0000 16.0000 2.0000 -1.0000 -2.0000 0 0.0000 -0.0000

0.0000

-1.0000 1.0000 5.0000 16.0000 2.0000 -1.0000 -2.0000 0 0.0000 -0.0000

0.0000

GRAPH:



10.FIR FILTER USING HAMMING WINDOW COMMAND:

METHOD-1

h=fir1(33,150/(1000/2),hamming(34)); figure(1); [m,w]=freqz(h,1,128); mag=20*log10(abs(m)); plot(w,mag); title('fir filter frequency response '); grid; n=1:30; f1=50;f2=300;f3=200;fs=1000; x=[]; x1=sin(2*pi*n*f1/fs); x2=sin(2*pi*n*f2/fs); x3=sin(2*pi*n*f3/fs); x=[x1 x2 x3]; figure(2); subplot(2,1,1); stem(x); title('input'); y=conv(h,x); -----------OR USE COMMAND y=filter(h,1,x); subplot(2,1,2); stem(y); title('output');

RESULT:

ans =



4

GRAPHS:



METHOD-2

wpa=input('enter passband freq in hz='); wsa=input('enter stopband freq in hz='); ws1=input('enter sampling freq in hz='); wpd=2*pi*wpa/ws1; wsd=2*pi*wsa/ws1; tb=wsd-wpd; N=ceil(6.6*pi/tb); wc=(wsd+wpd)/2; wc=wc/pi; hw=hamming(N+1); figure(1); stem(hw); title('fir filter window sequence hamming window'); h=fir1(N,wc,hamming(N+1)); figure(2); [m,w]=freqz(h,1,128); mag=20*log10(abs(m)); plot(w,mag); title('fir filter frequency response '); grid; figure(3); n=1:30; f1=50;f2=300;f3=200;fs=1000; x=[]; x1=sin(2*pi*n*f1/fs); x2=sin(2*pi*n*f2/fs);



x3=sin(2*pi*n*f3/fs); x=[x1 x2 x3]; subplot(2,1,1); stem(x); title('input'); y=conv(h,x);-----------OR USE COMMAND y=filter(h,1,x); subplot(2,1,2); stem(y); title('output');

RESULT:

ans =

4

enter passband freq in hz=100

enter stopband freq in hz=200

enter sampling freq in hz=1000

GRAPHS:



11. IIR FILTER DESIGN USING BUTTERWORTH AND CHEBYSHEV:

close all;



clear all; [b,a]=butter(2,150/(1000/2));---FOR CHEBYSHEV ONLY CHNGE butter TO cheby1 [num,den]=bilinear(b,a,1); n=1:30; f1=100;f2=300;f3=170;fs=1000; x=[]; x1=sin(2*pi*n*f1/fs); x2=sin(2*pi*n*f2/fs); x3=sin(2*pi*n*f3/fs); x=[x1 x2 x3]; figure(1); subplot(2,1,1); stem(x); title('input'); y=filter(num,den,x); subplot(2,1,2); stem(y); title('output'); figure(2); [m,w]=freqz(num,den,128); mag=20*log10(abs(m)); plot(w,mag); grid;

GRAPHS:

Frequency response



METHOD-2: close all; clear all; rp=1; rs=40; w1=800; w2=1200; ws=3600; aw1=2*pi*w1/ws; aw2=2*pi*w2/ws; pw1=2*tan(aw1/2); pw2=2*tan(aw2/2); [n,wc]=buttord(pw1,pw2,rp,rs,'s'); [b,a]=butter(n,wc,'s'); fs=1; [num,den]=bilinear(b,a,1); figure(1); [mag,freq1]=freqz(num,den,128); freq=freq1*ws/(2*pi); m=20*log10(abs(mag)); plot(freq,m) title('frequency response'); grid; n=1:30; f1=100;f2=300;f3=170;fs=1000; x=[]; x1=sin(2*pi*n*f1/fs); x2=sin(2*pi*n*f2/fs); x3=sin(2*pi*n*f3/fs); x=[x1 x2 x3];



figure(2); subplot(2,1,1); stem(x); title('input'); y=filter(num,den,x); subplot(2,1,2); stem(y); title('output'); figure(2);

GRAPHS:

Graph for input and output:



12.SOLVING A GIVEN DIFFERENCE EQUATION

Y(n)-y(n-1)+0.9y(n-2)=x(n)

12.1-IMPULSE RESPONSE

close all; clear all; N=input('length of response required'); b=[1]; a=[1 -1 0.9]; x=[1,zeros(1,N-1)]; n=0:1:N-1; h=filter(b,a,x); subplot(2,1,1); stem(n,x); title('impulse input'); xlabel('n'); ylabel('y(n)'); subplot(2,1,2); stem(n,h); title('impulse response'); xlabel('n'); ylabel('h(n)');

GRAPH FOR LENGTH:

length of response required 100



12.2-STEP RESPONSE: close all; clear all; N=input('length of response required'); b=[1]; a=[1 -1 0.9]; x=[ones(1,N)]; n=0:1:N-1; y=filter(b,a,x); subplot(2,1,1); stem(n,x); title('step input'); xlabel('n'); ylabel('u(n)'); subplot(2,1,2); stem(n,y); title('step response'); xlabel('n'); ylabel('y(n)');

GRAPH FOR LENGTH=50



12.3-STEADY STATE:

close all; clear all; N=input('length of response required'); b=[1]; a=[1 -1 0.8]; n=0:1:N-1; x=cos(0.05*pi*n); y=filter(b,a,x); subplot(2,1,1); stem(n,x); title('steady input'); xlabel('n'); ylabel('u(n)'); subplot(2,1,2); stem(n,y); title('steady response'); xlabel('n'); ylabel('y(n)');

RESULT FOR LENGTH=100



12.4-WITH INITIAL CONDITION:

b=[1/3 1/3 1/3]; a=[1 -0.95 0.9025]; Y=[-2 -3]; X=[1 1]; xic=filtic(b,a,Y,X); n=0:7; x=cos(pi*n/3); y=filter(b,a,x,xic); disp(y);

RESULT:

1.8075 4.3555 2.8398 -1.5664 -4.7176 -3.4014 1.3596 5.0281



PROGRAMMING IN CCS:

FOR CCS PROGRMMING USE THE CCS SOFTWARE:

1. To perform linear convolution for the given sequence. #include<stdio.h> #include<math.h> main() float h[4]={2,2,2,2}; float x[4]={1,2,3.4}; float y[10]; int xlen=4; int hlen=4; int N=xlen+hlen-1; int k,n; for(n=0;n<N;k++) { y[n]=0; for(k=0;k<hlen;k++) { if(((n-k)>=0)&((n-k)<xlen)) y[n]=y[n]+h[k]*x[n-k]; } printf("%f\t",y[n]); } } RESULT: 2 6 12 20 18 14 8

EXPERIMENT-2;

CIRCULAR CONVOLUTION FOR ANY TWO GIVEN SEQUENCE:

#include<stdio.h> #include<math.h> main() float x[5]={1,2,3,4,5}; float h[5]={1,2,3,4,5}; float y[10]; int N=5; int k,n,i; for(n=0;n<N;n++) { y[n]=0; for(k=0;k<N;k++) { i=(n-k)%N; if(i<0) i=i+N; y[n]=y[n]+h[k]*x[i]; } printf("%f\t",y[n]);



} }

RESULT:

41 51 51 46 36

3. COMPUTATION OF N-POINT DFT OF THE GIVEN EQUATION: #include<stdio.h> #include<math.h> main() { flot y[16]; float x[4]={1,3,2,5}; float w; int n,k,k1,N=8,xlen=4; for(k=0;k<2*N;k=k+2) { y[k]=0; y[k+1]=0; k=k1/2; for(n=0;n<xlen;n++) { w=-2*3.14*k1*n/N; y[k]=y[k]+x[n]*cos(w); y[k+1]=y[k+1]+x[n]*sin(w); } printf("%f+j%f\n",y[k+1]); } }

RESULT:

Result will come in complex form like-

11+j0.00 -0.40755+j-7.66 etc

4. TO FIND THE IMPULSE RESPONSE OF THE GIVEN FIRST ORDER/SECOND

ORDER SYSTEM:

#include<stdio.h> float x[60],y[60]; main() { float a1,a2,b0,b1,b2; int i,j,N=20; a1=-1.1430; a2=0.4128; b0=0.0675; b1=0.1349; b2=0.0675; x[0]=1; for(i=1;i<N;i++) {



y[j]=b0*x[j]; if(j>0) y[j]=y[j]+b1*x[j-1]-a1*y[j-1]; if((j-1)>0) y[j]=y[j]+b2*x[j-2]-a2*y[j-2]; printf("%f\t",y[j]); } }

RESULT: it will be only real valued as well as imaginary valued.



DIGITAL SIGNAL PROCESSING(DSP) VIVA QUESTIONS:

1. What is sampling theorem?

2. What do you mean by process of reconstruction.

3. What are techniques of reconstructions.

4. What do you mean Aliasing? What is the condition to avoid aliasing for sampling?

5. Write the conditions of sampling.

6. How many types of sampling there?

7. Explain the statement-

t= 0:0.000005:0.05

8. In the above example what does colon (:) and semicolon (;) denotes.

9. What is a) Undersampling b) nyquist plot c) Oversampling.

10. Write the MATLAB program for Oversampling.

11. What is the use of command ‘legend’?

12. Write the difference between built in function, plot and stem describe the function.

13. What is the function of built in function and subplot?

14. What is linear convolution?

15. Explain how convolution syntax built in function works.

16. How to calculate the beginning and end of the sequence for the two sided controlled

output?

17. What is the total output length of linear convolution sum.

18. What is an LTI system?

19. Describe impulse response of a function.

20. What is the difference between convolution and filter?

21. Where to use command filter or impz, and what is the difference between these two?

22. What is the use o function command ‘deconv’?

23. What is the difference between linear and circular convolution?

24. What do you mean by statement subplot (3,3,1).

25. What do you mean by command “mod” and where it is used?

26. What do you mean by Autocorrelation and Crosscorrelation sequences?

27. What is the difference between Autocorrelatio and Crsscorrelation.

28. List all the properties of autocorrelation and Crosscorrelaion sequence.

29. Where we use the inbuilt function ‘xcorr’ and what is the purpose of using this function?

30. How to calculate output of DFT using MATLAB?

31. What do you mean by filtic command, explain.

32. How to calculate output length of the linear and circular convolution.

33. What do you mean by built in function ‘fliplr’ and where we need to use this.

34. What is steady state response?

35. Which built in function is used to solve a given difference equation?

36. Explain the concept of difference equation.

37. Where DFT is used?

38. What is the difference between DFT and IDFT?

39. What do you mean by built in function ‘abs’ and where it is used?

40. What do you mean by phase spectrum and magnitude spectrum/ give comparison.



41. How to compute maximum length N for a circular convolution using DFT and

IDFT.(what is command).

42. Explain the statement- y=x1.*x2

43. What is FIR and IIR filter define, and distinguish between these two.

44. What is filter?

45. What is window method? How you will design an FIR filter using window method.

46. What are low-pass and band-pass filter and what is the difference between these two?

47. Explain the command – N=ceil(6.6*pi/tb)

48. Write down commonly used window function characteristics.

49. What is the matlab command for Hamming window? Explain.

50. What do you mea by cut-off frequency?

51. What do you mean by command butter, cheby1?

52. Explain the command in detail- [N,wc]=buttord(2*fp/fs,2*fstp/fs,rp,As)

53. What is CCS? Explain in detail to execute a program using CCS.

54. Why do we need of CCS?

55. How to execute a program using ‘dsk’ and ‘simulator’?

56. Which IC is used in CCS? Explain the dsk, dsp kit.

57. What do you mean by noise?

58. Explain the program for linear convolution for your given sequence.

59. Why we are using command ‘float’ in CCS programs.

60. Where we use ‘float’ and where we use ‘int’?

61. Explain the command- i=(n-k)%N

62. Explain the entire CCS program in step by step of execution.



*QUESTIONS WHICH WILL BE ASKED IN THE EXAMINATION WILL BE IN THE

FORM OF LIKE THIS

DSP LAB QUESTIONS

1. Write a MATLAB program so that output signal is sampled with a rate a) greater than

twice the max frequency content in the input signal and b) for equal to maximum

frequency content in the input signal. Given input signal is a cos function and the spacing

between the samples is 50µs and total time duration is 0.05 seconds.

2. Write a MATlAB program to find the system function of the causal LTI system with

input x(z)= 1+2z-1

+2z-2

+z-3

and output y(z)= 1+z-1

+2z-2

+z-3

so plot input, output and

impulse response.

3. Write a MATLAB program to find convolution of unit imulse function with X(z)= 1+3z-

1+4z

-2 and convoluted output length is equal to sum of two input lengths-1.

4. Write a MATLAB program to find the output of given system whose frequency response

is Y(z)= X(z).H(z) and given x(n)= (1,2,3,4), h(n)= (1,2,3,4) and output length is equal to

maximum length of x(n) and h(n).

5. Write a MATLAB program to find convolution of two given sequences in time domain

X1(z)= 1+2z-1

+3z-2

& X2(z)= 2+z-1

+4z-2

and convoluted output length is equal to sum of

two input lengths minus one.

6. Write a MATLAB program to find the similarities between the given sequence x(n)=

Sin(2*pi*n/N) for N=4 and the time shifted version of same sequences in terms of

convolution and write and verify a) Energy property b) periodicity property and draw the

graph for the same.

7. Write a program using MATLAB code for the received signal replected from the target is

the delayed uerreon of the transmitted signal. Assume delay in two time units. Assume

transmitted signal is {3, -1, 2, 1}.

8. Write a MATLAB program to find the similarities between the two given sequence X1

(n)= [1 3 -2 1 2 -1 4 4 2] and X2(n)= [2 -1 4 1 -2 3] is its time shifted version which is

shifted by two units, in terms of convolution and prove i) ϒxy[l]= ϒxy[-l] and 2) cross

correlation of two sequences x(n) and y(n)= x(n-k) is having peak at the value of k.

9. Write a MATLAB program to find the steady state response for the given difference

equation y(n)-0.8y(n-1)=x(n) and x(n)= cos(0.05*pi*n); n=0 to N-1 where N=20 and plot

the respective graph.

10. Write a MATLAB program to find the first 8 samples of the complete response y(n) for

the difference equation y[n]= 1/3 {x[n]+x[n-1]+x[n-2]}+0.95y[n-1]-0.9025y[n-2]; n>=0

where x(n)=cos(n*pi/3)u(n) and initial conditions are y[-1]=-2, y[-2]=-3, x[-1]=1, x[-

2]=1.

11. Write a MATLAB program to find the impulse response of a given difference equation

y(n)+0.8y(n-2)+0.6y(n-3)=x(n)+0.7x(n-1)+0.5x(n-2). Plot the graph for N=20.

12. Find steady state response using MATLAB for the difference equation y(n)-0.8y(n-1)=

x(n) and x(n)= Cos(wn); n=0 to N-1 where N=20.

13. Write a MATLAB program to find the multiplication of two frequencies domain

aperiodic signals in the domain x1=[1 1 1 1] and x2=[1 2 3 4].



14. Write a MATLAB program to find the multiplication of the two frequency domain

periodic signals in time domain x1=[1 1 1 1] and x2=[1 2 3 4].

15. Design an FIR filter for the given order of filter is 33 and cut-off frequency is 150Hz and

sampling frequency is 1KHz and having stop band attenuation 21dB. Implement the same

filter with assumed sinusoidal input.

16. Write a MATLAB program to design an FIR filter is 2 and cut-off frequency is 150 and

sampling frequency is 1KHz and having minimum stop band attenuation 44dB, Write a

MATLAB program to implement the same filter with assumed sine input.

17. Design an IIR filter for the pass band edge frequency w1=800 and stop band edge

frequency w2=1200. sampling frequency ws=3600, passband ripple 1dB and stopband

attenuation 40dB by using butterworth filter and maps it with bilinear transform. Find and

plot the magnitude and frequency response. Implement with 3 various sinusoidal input

signals of your own specification.

CCS PROGRAM:

18. Linear convolution of a given sequence.

19. Circular convolution of two sequences.

20. Computation of N-point DFT for given value of N.

21. Impulse response of given first order or second order filter.

dsp manual

Documents

verified output

convolution

point dft

sampling theorem

x1amp

dftamp

impulse response

xnsin