Electronics & Communication Dept. · 7 Write a MATLAB program to Compute Linear convolution with DFT 8 Write a MATLAB program to generate a) Generate the filter coefficients. b) 4-th

Electronics & Communication Dept.

1

Government Engineering College, Bharuch

Electronics and Communication Department

Semester 7

Lab Manual

For

Digital Signal Processing (171003)

Academic Term: 15-6-2015 to 15-10-2015


2

Index

Sr. No.

Title Page No.

Date Sign

1 Generate the following sequence with MATLAB

a) UNIT Sample sequence

b) Unit step sequence

c) Ramp sequence

2 Generate the following sequence with MATLAB.

a) Complex exponential sequence.

b) Sine, Cosine, Square wave at 5 Hz.

3 Write a MATLAB program to generate

a) to plot Impulse response computation using

stem function.

b) Signal smoothing by moving- average Filter.


a) Computation of cross-correlation of a

sequence

b) Computation of Autocorrelation of a

sequence.

c) Linear convolution of a two sequence


a) Partial fraction expansion to Rational Z-

transform

b) Determination of the rotational Z-trnsform

from its poles and zeros and vice versa. c) Determination of the factored form of a

Rational Z-transform. d) Power series expansion of a Rational Z-

transform.


a) DFT (Discrete Fourier Transform)

computation.

b) IDFT (Inverse Discrete Fourier Transform)

computation.

7 Write a MATLAB program to Compute Linear

convolution with DFT


a) Generate the filter coefficients.

b) 4-th order analog Butterworth low pass filter.


a) Butterworth low pass filter.

b) Elliptic low pass filter.

c) Type 1 chebyshev Low pass filter.


3


a) Estimation of FIR Filter Order using

remezord.

b) IIR Butterworth Band pass Filter.

c) Type 1 Chebyshev IIR High pass Filter

Design

d) Elliptic IIR Low pass Filter Design.


a) Generation of rectangular, hamming,

hanning, blackman and Kaiser Window.

b) Low pass filter Design Using the Kaiser

Window.

c) Coefficient Quantization Effects on the

Frequency Response of a Cascade Form IIR

Filter


4

EXP.1 Generate the following sequence with MATLAB



c) Ramp sequence

Program:


clc;

clear all;

close all;

n=-50:1:50;

x=[zeros(1,50),1,zeros(1,50)];

stem(n,x);

-50 -40 -30 -20 -10 0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

samples---->

am

plitu

de--

----

->

Unit impulse sequence


5


clc;

clear all;

close all;

n=-50:1:50;

x=[zeros(1,50),ones(1,51)];

stem(n,x);

-50 -40 -30 -20 -10 0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

samples---->

am

plit

ude--

----

->

Unit step sequence


6

c) Unit Ramp Sequence

clc;

clear all;

close all;

n=-50:1:50;

x=zeros(1,101)

t=1:1:102;

for t=1:1:101

if t>=51

x(1,t)=(t-51);

else

x(1,t)=0;

end

end

stem(n,x)

Output:

-50 -40 -30 -20 -10 0 10 20 30 40 500

5

10

15

20

25

30

35

40

45

50

samples---->

am

plit

ude--

----

->

Ramp sequence


7

EXP.2 Generate the following sequence with MATLAB.

a) Complex exponential sequence.

clc;

clear all;

a=input('Type in real exponent : ');

b=input('Type in complex exponent : ');

c=a+b*i;

k=input('Type in the gain constant : ');

N=input('Type in length of sequence : ');

n=1:N;

x=k*exp(c*n);

subplot(2,1,1)

stem(n-1,real(x));

xlabel('time index n');ylabel('amplitude');

title('real part');

subplot(2,1,2)

stem(n-1,imag(x));

xlabel('time index n');ylabel('amplitude');

title('imaginary part');


8

INPUT:

Type in real exponent : -1/12

Type in complex exponent : pi/6

Type in the gain constant : 4

Type in length of sequence : 40

OUTPUT:


9

b) Sine, Cosine, Sinc wave at 5 Hz. clc;

clear all;

f=input('Enter the value of signal freq: ');

fs=input('Enter the value of sampling freq: ');

a=input('Enter the amplitude of signal:');

t=0:1/fs:1;

x=a*sin(2*pi*f*t);

subplot(3,1,1);plot(x);

grid on;

xlabel('Time index n samples'); ylabel('Amplitude');

y=a*cos(2*pi*f*t);

subplot(3,1,2);plot(y);

grid on;


z=a*sinc(2*pi*f*t);

subplot(3,1,3);plot(z);

grid on;



10

INPUT:

Enter the value of signal freq: 5

Enter the value of sampling freq: 100

Enter the amplitude of signal:10

OUTPUT:


11

EXP.3 Write a MATLAB program to generate

a) Programme to plot Impulse response computation using stem function.

clc;

clear all;

n=input('Enter the no of samples: ');

p=[0.8 0.44 -0.36 -0.02];

d=[1 0.7 -0.45 -0.6];

imp=[1 zeros(1,n-1)];

stp=[ones(1,n)];

k=0:1:n-1;

ir=filter(p,d,imp);

subplot(2,1,1)

stem (k,ir);

title('impulse response');

grid on;

axis([0 50 -1 1.5]);

str=filter(p,d,stp);

subplot(2,1,2)

stem (k,str);

title('step response');

grid on;

axis([0 50 -0.5 1.5]);


12

INPUT:-

Enter the no of samples: 41

OUTPUT:-


13

b) Signal smoothing by moving- average Filter.

clc

clear all;

w=input('Enter window size:');

fs=input('Enter sampling freq:');

f=input('Enter freq:');

t=0:1/fs:1;

x=sin(2*pi*f*t);

e=0.5*randn(1,fs+1);

xe=x+e;

for n=1:fs-w

xblk=xe(1,n:n+w-1);

y(n)=(1/w)*sum(xblk);

end

subplot 211; plot(xe);title('Noisy signal');grid on;

subplot 212; plot(y);title('filtered signal');grid on;


14

INPUT:-

Enter window size: 200

Enter sampling freq: 10000

Enter freq: 10

OUTPUT:-


15

EXP. 4 Write a MATLAB program to compute.

a) Computation of cross-correlation of a sequence

clc;

x=input('Enter the first frequency: ');

h=input('Enter the second frequency:');

y=xcorr(x,h);

disp(y);

figure

stem(y);

INPUT:

Enter the first frequency: [5 4 2 6]

Enter the second frequency:[ 0 1 2 3]

15 22 19 26 14 6 0

OUTPUT:


16

b) Computation of Autocorrelation of a sequence.

clc;

clear all;

x=input('Enter the first frequency: ');

y=xcorr(x);

disp(y);

figure

stem(y);

grid on;

INPUT:

Enter the first frequency: [2 4 7 3]

6.0000 26.0000 57.0000 78.0000 57.0000 26.0000 6.0000

OUTPUT:


17

c) Linear convolution of a two sequence clc;

clear all;

a=input('Type in the first sequence: ');

b=input('Type in the second sequence: ');

c=conv(a,b);

M=length(c)-1;

n=0:1:M;

disp('output seq=');disp(c);

stem(n,c);

xlabel('time index n');

ylabel('amplitude');


18

INPUT:

Type in the first sequence [1 2 5 4]

type in the second sequence[1 5 4 9]

Output seq=

1 7 19 46 58 61 36

OUTPUT:


19

EXP.5 Write a MATLAB program for.

a) Partial fraction expansion to Rational Z-transform

clc;

clear all;

num=input('type in numeractor coeff');

den=input('type in denominator coeff');

[r,p,k]=residuez(num,den);

disp('residues');disp(r);

disp('Poles');disp(p);

disp('Constant');disp(k);

INPUT:

Type in numerator coeff [3 4 3]

Type in denominator coeff [1 3 4]

OUTPUT:

Residues

1.1250 + 0.6142i

1.1250 - 0.6142i

Poles

-1.5000 + 1.3229i

-1.5000 - 1.3229i

Constant

0.7500


20

b) Determination of the rotational Z-trnsform from its poles and zeros and vice versa.

clc

clear all;

num = input('type in the numerator coeff');

den = input('type in the denominator coeff');

[z,p,k]=tf2zp(num,den);

m = abs(p);

disp('zeros ar at');disp(z);

disp('poles ar at');disp(p);

disp('gain constant');disp(k);

disp('radius of poles');disp(m);

sos = zp2sos(z,p,k);

disp('second order sections ');disp(real(sos));

zplane(num,den);


21

INPUT:

type in the numerator coeff[1 2 3]

type in the denominator coeff[3 4 2]

OUTPUT:

zeros ar at

-1.0000 + 1.4142i

-1.0000 - 1.4142i

poles ar at

-0.6667 + 0.4714i

-0.6667 - 0.4714i

gain constant

0.3333

radius of poles

0.8165

0.8165

second order sections

0.3333 0.6667 1.0000 1.0000 1.3333 0.6667


22

c) Determination of the factored form of a Rational Z-transform.

clc;

clear all;

z= input('type in the zeroes:');

p= input('type in the poles:');

k= input('type in the constant:');

[num,den]=zp2tf(z,p,k)

disp(num);

disp(den);

INPUT:]

type in zeros: 3

type in the poles:3

type in the constant:4

OUTPUT:

num =

4 -12

den =

1 -3

4 -12

1 -3


23

d) Power series expansion of a Rational Z-transform.

clc;

clear all;

L=input('type in the length of output vector');

num=input('enter num poly: ');

den=input('enter den poly: ');

[y,t]=impz(num,den,L);

disp('coeff of the power series expansion');

disp(y);

INPUT:

type in the length of output vector[1 2 3]

enter num poly: [2 3 4]

enter den poly: [1 3 6]

OUTPUT:

coeff of the power series expansion

-3

1

15


24

EXP.6 Write a MATLAB program to compute.

a) DFT (Discrete Fourier Transform) computation. clc;

clear all;

N=input('Enter the value of N:');

fs=input('Enter the value of sampling freq:');

f=input('Enter the value of signal freq:');

t=0:1/fs:1;

x=sin(2*pi*f*t);

y=fft(x,N);

ymag=abs(y(1,1:N/2));

yangle=angle(y(1,1:N/2));

subplot 411; plot(x);title('input signal');

subplot 412; stem(ymag);title('Magnitude Spectrum');

subplot 413; stem(yangle);title('Phase Spectrum');

subplot 414; plot(ymag);title(' Magnitude Spectrum');


25

INPUT:

Enter the value of N:100

Enter the value of sampling freq:100

Enter the value of signal freq:10

OUTPUT:


26

b) IDFT (Inverse Discrete Fourier Transform) computation.

clc;

clear all;

N=input('Enter the value of N:');

fs=input('Enter the value of sampling freq:');

f=input('Enter the value of signal freq:');

t=0:1/fs:1;

x=sin(2*pi*f*t);

y=fft(x,N);

z=ifft(y,N);

z=real(z);

ymag=abs(y(1,1:N/2));

yangle=angle(y(1,1:N/2));

subplot 411; plot(x);title('input signal');

subplot 412; stem(ymag);title('Frequency Spectrum');

subplot 413; stem(yangle);title('Phase Spectrum');

subplot 414;plot(z);title('inverse DFT');


27

INPUT:

Enter the value of N: 200

Enter the value of sampling freq: 200

Enter the value of signal freq: 20

OUTPUT:


28


a) Computation of Linear convolution with DFT

clc;

clear all;

g=input('Type in the first sequence:');

h=input('Type in the second sequence:');

ga=[g zeros(1,length(h)-1)];

ha=[h zeros(1,length(g)-1)];

G=fft(ga);

H=fft(ha);

Y=G.*H;

y=ifft(Y);

subplot 411; stem(g); title('First sequence');

subplot 412; stem(h); title('second sequence');

subplot 413; stem(y); title('New sequence');

subplot 414; plot(y); title('New sequence');


29

INPUT:

Type in the first sequence:[1 2 5]

Type in the second sequence:[ 6 7 8]

OUTPUT:


30


a) Generate the filter coefficients.

clc;

clear all;

h1=ones (1,5)/5;

h2=ones(1,14)/14;

w=0:pi/255:pi;

H1=freqz(h1,1,w);

H2=freqz(h2,1,w);

m1=abs(H1);m2=abs(H2);

plot(w/pi,m1,'r-',w/pi,m2,'b--');

grid on;

ylabel('Magnitute ');xlabel('\omega/pi');

legend('r','M=5','b--','M=18');

ph1=angle(H1)*180/pi;

ph2=angle(H2)*180/pi;

plot(w/pi,ph1,w/pi,ph2);

grid on;

ylabel('phase and angle ');xlabel('\omega/pi');

legend('r','M=5','b--','M=18');


31

OUTPUT:

Magnitude Plot

Phase Plot


32

b) 4-th order analog Butterworth low pass filter.

clc;

clear all;

[z,p,k] = buttap(4);

disp('Poles are at');disp(p);

[pz, pp] = zp2tf(z, p, k);

disp('Numerator polynomial'); disp(pz)

disp('Denominator polynomial'); disp(real(pp))

omega = [0: 0.01: 5];

h = freqs(pz,pp,omega);

plot (omega,20*log10(abs(h)));grid

xlabel('Normalized frequency'); ylabel('Gain, dB');


33

OUTPUT:

Poles are at

-0.38268343236509 + 0.92387953251129i

-0.38268343236509 - 0.92387953251129i

-0.92387953251129 + 0.38268343236509i

-0.92387953251129 - 0.38268343236509i

Numerator polynomial

0 0 0 0 1

Denominator polynomial

Columns 1 through 2

1.00000000000000 2.61312592975275

Columns 3 through 4

3.41421356237309 2.61312592975275

Column 5

1.00000000000000


34


a) Butterworth low pass filter.

clc;

clear all;

N=input('Type in filter order=');

wn=input('3-dB cutoff frequency=');

%Determine the transfer function

[num,den]=butter(N,wn,'s');

%compute and plot the frequency response

omega=[0:1200*pi];

h=freqs(num,den,omega);

plot(omega/(2*pi),20*log10(abs(h)));grid on;

xlabel('Frequency,hz');ylabel('Gain,dB');


35

INPUT:

Type in filter order=10

3-dB cutoff frequency=400

OUTPUT:


36

b) Elliptic low pass filter.

clc;

clear all;

N = input('Order = ');

Fp = input('Passband edge frequency in Hz = ');

Rp = input('Passband ripple in dB = ');

Rs = input('Minimum stopband attenuation in dB = ');

% Determine the coefficients of the transfer function

[num,den] = ellip(N,Rp,Rs,2*pi*Fp,'s');

% Compute and plot the frequency response

omega = [0: 200: 12000*pi];

h = freqs(num,den,omega);

plot (omega/(2*pi),20*log10(abs(h)));

xlabel('Frequency, Hz'); ylabel('Gain, dB');


37

INPUT:

Order = 5

Passband edge frequency in Hz = 2000

Passband ripple in dB = 1

Minimum stopband attenuation in dB = 40

OUTPUT:


38

c) Type 1 chebyshev Low pass filter.

clc;

clear all;




% Determine the coefficients of the transfer function

[num,den] = cheby1(N,Rp,Fp,'s');

% Compute and plot the frequency response

omega = [0: 200: 12000*pi];


plot (omega/(2*pi),20*log10(abs(h)));grid on;



39

INPUT:

Order = 3



OUTPUT:


40


a) Estimation of FIR Filter Order using remezord.

clc;

clear all;

fedge = input('Type in the bandedges = ');

mval = input('Desired magnitude values in each band = ');

dev = input('Allowable deviation in each band = ');

FT = input('Type in the sampling frequency = ');

[N,fpts,mag,wt]=remezord(fedge,mval,dev,FT);

fprintf('Filter order is %d \n',N);

end;

INPUT:

Type in the bandedges = [1500 2000]

Desired magnitude values in each band = [1 0]

Allowable deviation in each band = [0.01 0.1]

Type in the sampling frequency = 8500

OUTPUT:

Filter order is 23


41

b) IIR Butterworth Band pass Filter.

clc;

clear all;

w0=input('Enter the value of center frequency:');

bw=input('Enter the value of bandwidth:');

alpha=(1-sin(bw))/cos(bw);

beta=cos(w0);

k=(1-alpha)/2;

num=[k 0 -k];

den=[1-beta*(1+alpha) alpha];

[h,w]=freqz(num,den);

plot(w/pi,abs(h));grid on;


42

INPUT:

Enter the value of center frequency:3

Enter the value of bandwidth:0.5

OUTPUT:


43

c) Type 1 Chebyshev IIR High pass Filter Design

clc;

clear all;

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

Rp=input('Enter the passband ripple: ');

Wn=input('enter the pass band edge:');

[b,a]=cheby1(N,Rp,Wn,'high');

disp('numerator polynomial');

disp(b);

disp('denominator polynomial');

disp(a);

pause;

w=0:0.01/pi:pi;

h=freqz(b,a,w);

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

plot(w/pi,gain); axis([0 1 -50 5]); grid on;

xlabel('Normalized frequency');

ylabel('Gain,dB');


44

INPUT:

Enter the order of the filter:8

Enter the passband ripple: 3

enter the pass band edge:0.4

OUTPUT:

numerator polynomial

0.0084 -0.0335 0.0502 -0.0335 0.0084

denominator polynomial

1.0000 2.3741 2.7057 1.5917 0.4103


45

d) Elliptic IIR Low pass Filter Design.

clc;

clear all;




Rs = input('Minimum stopband attenuation in dB = ');

[num,den] = ellip(N,Rp,Rs,2*pi*Fp,'s');

omega = [0: 20: 120*pi];


plot (omega/(2*pi),20*log10(abs(h))); grid on;



46

INPUT:

Order = 8



Minimum stopband attenuation in dB = 40

OUTPUT:


47


a) Generation of rectangular,hamming,hanning,blackman and kaiser window.

clc;

clear all;


x1=hann(N);

x2=hamming(N);

x3=bartlett(N);

x4=blackman(N);

x5=triang(N);

x6=kaiser(N);

plot(x1);hold on; grid on;

plot(x2,'*');

plot(x3,'.');

plot(x4,'x');

plot(x5,'+');

plot(x6,'^');


48

INPUT:

Order = 60

OUTPUT:


49

b) Low pass filter Design Using the Kaiser Window.

clc;

clear all;

fpts = input('Type in the bandedges = ');

mag = input('Type in the desired magnitude values = ');

dev = input('Type in the ripples in each band = ');

type= input('Type in the sampling frequency = ');

[N,Wn,beta,ftype] = kaiserord(fpts,mag,dev,type)

kw = kaiser(N+1,beta);

b = fir1(N,Wn, kw);

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

plot(omega/pi,20*log10(abs(h)));grid;

xlabel('\omega/\pi'); ylabel('Gain, dB');


50

INPUT:

Type in the bandedges = [1500 2000]

Type in the desired magnitude values = [1 0]

Type in the ripples in each band = [0.01 0.1]

Type in the sampling frequency = 8000

OUTPUT:

N =

36

Wn =

0.4375

beta =

3.3953

ftype =

low


51

c) Coefficient Quantization Effects on the Frequency Response of a Cascade Form IIR Filter

clc;

clear all;

[z,p,k] = ellip(5,0.4,50,0.4);

[b,a] = zp2tf(z,p,k);

bq=roundn(b,-2);

aq=roundn(a,-2);

[h,w] = freqz(b,a,512); g = 20*log10(abs(h));

[hq,w] = freqz(bq,aq,512); gq = 20*log10(abs(hq));

plot(g);hold on; plot(gq,'r');

grid on;

OUTPUT:

Documents

Electronics & Communication Dept. · 7 Write a MATLAB program to Compute Linear convolution with DFT 8 Write a MATLAB program to generate a) Generate the filter coefficients. b) 4-th