dsp lab manual
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(Affiliated to Kurukshetra University Kurukshetra)(Approved by AICTE, New Delhi)
Practical ReportOn
MATLAB (DIGITAL SIGNAL PROCESSING LAB)
ECE-490E
Submitted for partial fulfillmentOf B. Tech. in
ELECTRONICS AND COMMUNICATION ENGINEERING
SUBMITTED TO: SUBMITTED BY:
Er. Naresh Kumar Rashi GuptaH.O.D. ECE Department 4309102
ECE 3rd Year
INDEX
S.NO. EXPERIMENT NAME DATE PAGE NO.
SIGNATURE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
EXPERIMENT-1
AIM: - Write a program to plot the following functions : a)impulse function
b)unit step c)unit ramp d) exponential e) sinusoidal.
REQUIREMENT: - Computer installed with MATLAB 7.1
PROGRAM CODE: -
t=(-1:.01:1);%range for time or division of x-axis
%To plot unit step
z=[zeros(100,1);ones(101,1)];
subplot(4,1,2);
stem(t,z);
xlabel('time');
ylabel('amp');
title('Fig-2 unit STEP Signal');
%To plot sin wave
x1=sin(2*pi*10*t);
subplot(4,1,4);
plot(t,x1);
xlabel('time');
ylabel('amp');
title('Fig-4 SIN Signal');
%To plot unit impulse signal
y=[zeros(100,1); 1 ;zeros(100,1)];
subplot(4,1,1);
stem(t,y);
xlabel('time');
ylabel('amp');
title('Fig-1 unit IMPLUSE Signal');
%To plot Ramp signal
subplot(4,1,3);
plot(t,t);
xlabel('time');
ylabel('amp');
title('Fig-3 RAMP Signal');
OUTPUT:
RESULT: - The Plot of various standard signals has been studied using MATLAB program.
EXPERIMENT-2
AIM: - To study the Modulation Process.
REQUIREMENT: - Computer installed with MATLAB 6.1
PROGRAM CODE: -
n=-10:1:10;
k=0:1:99;
f=10/158;
x=10-abs(n);
X=x*(exp(-j*2*pi/100).^(n'*k));
c=cos(2*pi*f*n);
z=x.*c;
Z=z*(exp(-j*2*pi/100).^(n'*k));
y=1/2*((exp(-j*2*pi*f*n).*x)+(exp(j*2*pi*f*n).*x));
Y=y*(exp(-j*2*pi/100).^(n'*k));
Error=Y-Z;
subplot(2,4,1);
stem(n,x);
title('Modulating Function');
xlabel('Time');
ylabel('Values');
subplot(2,4,2);
stem(k,X);
title('DFT of Modulating Function');
xlabel('Time');
ylabel('Values');
subplot(2,4,3);
plot(n,c);
title('CarrierFunction');
xlabel('Time');
ylabel('Values');
subplot(2,4,4);
stem(n,z);
title('Modulated Function');
xlabel('Time');
ylabel('Values');
subplot(2,4,5);
stem(k,Z);
title('DFT of Modulated Function');
xlabel('Time');
ylabel('Values');
subplot(2,4,6);
stem(n,y);
title('Modulated Function in exponential form');
xlabel('Time');
ylabel('Values');
subplot(2,4,7);
stem(k,Y);
title('DFT of Modulated Function in exponential form');
xlabel('Time');
ylabel('Values');
subplot(2,4,8);
stem(k,Error);
title('Error Plot');
xlabel('Time');
ylabel('Values');
GRAPHS: -
Graphs for the Process of Modulation
RESULT: - The Modulation Process has been studied using a MATLAB program.
EXPERIMENT: 3
AIM: - To study the Aliasing Effect.
REQUIREMENT: - Computer installed with MATLAB 6.1
PROGRAM CODE: -n=0:1:99;
f=5/158;
f1=1/158;
f2=10/158;
f3=50/158;
x=sin(2*pi*f*n);
c1=cos(2*pi*f1*n);
c2=cos(2*pi*f2*n);
c3=cos(2*pi*f3*n);
y1=x.*c1;
y2=x.*c2;
y3=x.*c3;
subplot(4,2,1);
plot(n,x);
title('Modulating Function');
xlabel('Values');
ylabel('Amplitude');
subplot(4,2,2);
plot(n,c1);
title('Carrier Function 1');
xlabel('Values');
ylabel('Amplitude');
subplot(4,2,3);
plot(n,c2);
title('Carrier Function 2');
xlabel('Values');
ylabel('Amplitude');
subplot(4,2,4);
plot(n,c3);
title('Carrier Function 3');
xlabel('Values');
ylabel('Amplitude');
subplot(4,2,5);
plot(n,y1);
title('Frequency<Nyquest Rate (aliasing)');
xlabel('Values');
ylabel('Amplitude');
subplot(4,2,6);
plot(n,y2);
title('Frequency=Nyquest Rate');
xlabel('Values');
ylabel('Amplitude');
subplot(4,2,7);
plot(n,y3);
title('Frequency>Nyquest Rate( no aliasing)');
xlabel('Values');
ylabel('Amplitude');
GRAPHS: -
Graphs for the Aliasing Effect
RESULT: - The Aliasing Effect has been studied.
EXPERIMENT-4
AIM: - Write a program to find the DFT of the sequence
REQUIREMENT: - Computer installed with MATLAB 7.1
PROGRAM CODE: -
clear all;x=[1 1 1 ]; %Given sequenceN=50;L=length(x);if(N<L) error('N must be less than L');end;x1=[x,zeros(1,N-L)]; %Appending of Zerosj = sqrt(-1); for k=0:N-1 %twiddle factor calculation for n=0:N-1 W=exp(-j*2*pi*n*k/N); x2(k+1 ,n+1)= W; endend X=x1*x2.'; %Computation of DFT by Dot product of Twiddle factor matrix & sequence magx=abs(X); anglex=angle(X); k=0:N-1; %To plot Mag. & Angle of output sequence subplot(2,1,1); stem(k,magx); xlabel('k'); ylabel('Mod of X'); title('Fig-1(a)Magnitude plot'); subplot(2,1,2); stem(k,anglex); xlabel('k'); ylabel('Angle of X'); title('Fig-1(b)Phase plot');
OUTPUT:
RESULT: - The DFT of the given discrete signal can be find out correctly with the help of this program code, it is checked with the help of above graphical results and manual calculations.
EXPERIMENT-5
AIM: - Write a program to plot the IDFT of a Sequence.
REQUIREMENT: - Computer installed with MATLAB 7.1
PROGRAM CODE: -
%To compute
clear all;
xk=[6,2i-2,-2,-2i-2]; %given Sequence
N=length(xk); %function to find length of sequence
for k=0:1:N-1 %loop from 0 to length(xk)-1
for n=0:1:N-1 %loop from 0 to length(xk)-1
p=exp(i*2*pi*n*k/N); %twiddle factor
x2(k+1,n+1)=p; %twiddle factor matrix
end %end of loop 1
end %end of loop 2
xn=((xk*x2.')./N); % Computation of IDFT
magx=abs(xn); %To compute Magnitude
anglex=angle(xn); % To compute angle
%To plot the Magnitude and Angle of a sequence
k=0:N-1;
subplot(2,1,1);
stem(k,magx);
xlabel('k');
ylabel('Mod of X');
title('Fig-1(a)Magnitude plot');
subplot(2,1,2);
stem(k,anglex);
xlabel('k');
ylabel('Angle of X');
title('Fig-1(b)Phase plot');
OUTPUT:
Result: The IDFT of the given DFT signal can be find out correctly with the help of this program code, it is checked with the help of above graphical results and manual calculations.
EXPERIMENT-6
AIM: - Write a program to study of Windows.
REQUIREMENT: - Computer installed with MATLAB 7.1
PROGRAM CODE: -N=64;
n=[0:1:N-1];
% Study of Rectangular Window
Wr=rectwin(N);
% Bartlett Window(Triangular Window
Wb=triang(N);
% Hamming Window
Wh=hamming(N);
% Blackman Window
Wbl=Blackman(N);
subplot(2,1,1),plot(n,Wr,n,Wb,n,Wh,n,Wbl);grid
legend('Rectangular','Bartlett','Hamming','Blackman',4);
xlabel('n');
ylabel('Amplitude');
title('Window Characteristics');
Wrdb=20*log(Wr);
Wbdb=20*log(Wb);
Whdb=20*log(Wh);
Wbldb=20*log(Wbl);
subplot(2,1,2),plot(n,Wrdb,n,Wbdb,n,Whdb,n,Wbldb);grid
legend('Rectangular','Bartlett','Hamming','Blackman',4);
xlabel('n');
ylabel('Amplitude in db');
title('Window Characteristics in db');
OUTPUT:
Result: The various windows have been studied with the help of the above program code in this experiment.
Experiment: 7
AIM: To design Butterworth Band Pass Filter.
clear all;
alphap=2; %Passband Attenuation in db
alphas=20; %Passband Attenuation in db
wp=[.2*pi,.4*pi %Passband Frequency In Radian
ws=[.1*pi,.5*pi %Stopband Frequency In Radian
[n,wn]=buttord(wp/pi,ws/pi,alphap,alphas);
[b,a]=butter(n,wn); %To design Butterworth filter
w=0.1:.01:pi;
[h,om]=freqz(b,a,w); %Returns the frequency response
vector h calculated
%at the frequencies (in radians per sample) supplied by the vector w
% To plot the Response w.r.t Normalized Freq.
m=20*log(abs(h));
an=angle(h);
subplot(2,1,1);
plot(om/pi,m);
grid;
Ylabel('Gain in DBn');
Xlabel('Normalized Freq.');
subplot(2,1,2);
plot(om/pi,an);
grid;
Ylabel('Phase in Radia');
Xlabel('Normalized Freq.');
Output:
RESULT: - The Plot of Butterworth Band Pass Filter has been studied using MATLAB
program.
Experiment: 8
AIM: To design Butterworth bandreject Filter
clear all;
alphap=2; %Passband Attenuation in db
alphas=20; %Passband Attenuation in db
wp=[.2*pi,.4*pi]; %Passband Frequency In Radian
ws=[.1*pi,.5*pi]; %Stopband Frequency In Radian
[n,wn]=buttord(wp/pi,ws/pi,alphap,alphas);%Function for Filter for order and cutoff freq.
[b,a]=butter(n,wn,'stop'); %To design Butterworth filter
w=0.1:.01:pi;
[h,om]=freqz(b,a,w); %Returns the frequency response
vector h calculated
%at the frequencies (in radians per sample) supplied by the vector w
% To plot the Response w.r.t Normalized Freq
m=20*log(abs(h));
an=angle(h);
subplot(2,1,1);
plot(om/pi,m);
grid;
Ylabel('Gain in DBn');
Xlabel('Normalized Freq.');
subplot(2,1,2);
plot(om/pi,an);
grid;
Ylabel('Phase in Radia');
Xlabel('Normalized Freq.');
Output:-
RESULT: - The Plot of Butterworth Band Reject Filter has been studied using
MATLAB program.
Experiment: 9
AIM: To design Butterworth High Pass Filter
clear all;
alphap=.2;%Passband Attenuation in db
alphas=30;%Passband Attenuation in db
fp=400;%Passband Frequency In Hz
fs=800;%Stopband Frequency In Hz
F=2000;%Sampling Frequency In Hz
omp=2*fp/F;% Frequency in Radians
oms=2*fs/F;% Frequency in Radians
[n,wn]=buttord(omp,oms,alphap,alphas);%Function for Filter
[b,a]=butter(n,wn,'high');
w=0:.01:pi;
[h,om]=freqz(b,a,w); %Returns the frequency response vector h calculated
%at the frequencies (in radians per sample) supplied by the vector w
% To plot the Response w.r.t Normalized Freq
m=20*log(abs(h));
an=angle(h);
subplot(2,1,1);
plot(om/pi,m);
grid;
Ylabel('Gain in DB');
Xlabel('Normalized Freq.');
subplot(2,1,2);
plot(om/pi,an);
grid;
Ylabel('Phase in Radian');
Xlabel('Normalized Freq.');
Output:-
RESULT: - The Plot of Butterworth High Pass Filter has been studied using MATLAB
program.
Experiment: 10
AIM:To design Butterworth Low Pass Filter.
clear all;
alphap=2;%Passband Attenuation in db
alphas=20;%Passband Attenuation in db
fp=400;%Passband Frequency In Hz
fs=800;%Stopband Frequency In Hz
F=2000;%Sampling Frequency In Hz
omp=2*fp/F;% Frequency in Radians
oms=2*fs/F;% Frequency in Radians
[n,wn]=buttord(omp,oms,alphap,alphas);%Function for Filter
[b,a]=butter(n,wn);
w=0:.01:pi;
[h,om]=freqz(b,a,w,'whole'); %Returns the frequency response vector h calculated
%at the frequencies (in radians per sample) supplied by the vector w
% To plot the Response w.r.t Normalized Freq
m=20*log(abs(h));
an=angle(h);
subplot(2,1,1);
plot(om/pi,m);
grid;
Ylabel('Gain in DB');
Xlabel('Normalized Freq.');
subplot(2,1,2);
plot(om/pi,an);
grid;
Ylabel('Phase in Radian');
Xlabel('Normalized Freq.');
Output:
RESULT: - The Plot of Butterworth Low Pass Filter has been studied using MATLAB
program.
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