Digital Signal Processing Lab
ADVANCED DIGITAL SIGNAL
PROCESSING LAB
Submitted to:
Submitted by:
Dr. Debabrata Ghosh
Twinkle Bansal
801961005
ME-ECE
1|Page
Digital Signal Processing Lab
INDEX
S. No.
Name of the Experiment
1.
Write a program
Practical Data
Submission Date
Remarks
a. To generate unit impulse, unit step, and
Signum function.
b. To generate the square waves (both
continuous and discrete plot) with user
input frequencies and duty cycle.
c. To generate the sinusoidal signal with
user input multiple frequencies,
amplitude, and its phase.
2.
Write a program
a. To determine N-point DFT of the user
input sequence (without using built in
command) and plot its magnitude and
phase spectrum.
b. Compare the IDFT of the results
obtained in (a).
3.
WAP to determine the Linear Convolution
(without using inbuilt command) of any two
discrete sequences.
4.
WAP to determine the Circular Convolution
(without using inbuilt command) of user
defined two discrete sequences.
5.
WAP to determine the Circular Convolution
of any two discrete sequences using DFT
and IDFT.
6.
WAP to determine the time domain and
frequency domain response of fixed
windows by taking N=25.
2|Page
Digital Signal Processing Lab
7.
WAP to design the FIR Low filter using
windows by user parameters.
8.
Write a program to perform the decimation
without using in-built function.
3|Page
Digital Signal Processing Lab
Experiment No-1
AIM:
Write a program
a) To generate unit impulse, unit step, and Signum function.
b) To generate the square waves (both continuous and discrete plot) with user input
frequencies and duty cycle.
c) To generate the sinusoidalsignal with user input multiple frequencies, amplitude, and its
phase.
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE: Part 1 (a)
%To generate unit impulse, unit step, and Signum function.
clear all
close all
clc
% Unit Impulse Function
x = -10:1:10;
y = [zeros(1,10) ones(1,1) zeros(1,10)];
subplot(3,1,1)
stem(x,y)
title('Unit Impulse Function (801961005)')
xlabel('Time')
ylabel('Amplitude')
% Unit Step Function
x1 = -10:1:10;
y1 = [zeros(1,10) zeros(1,1) ones(1,10)];
subplot(3,1,2)
4|Page
Digital Signal Processing Lab
stem(x1,y1)
title('Unit Step Function (801961005)')
xlabel('Time')
ylabel('Amplitude')
% Signum Function
x3 = -10:1:10;
y3 = sign(x3);
subplot(3,1,3)
stem(x3,y3)
title('Signum Function (801961005)')
xlabel('Time')
ylabel('Amplitude')
OUTPUT: Part 1 (a)
5|Page
Digital Signal Processing Lab
MATLAB CODE: Part 1 (b)
%%
clear all
close all
clc
%-------- Case1: Duty cycle=25% and frequency=5Hz --------%
% Continous Plot
% Time
t = 1:0.01:10;
duty_cycle = 25;
freq = 5;
x = square(2*pi*freq*t,duty_cycle);
subplot(3,2,1)
plot(t,x)
title('Continous => Duty cycle=25% and frequency=5Hz (801961005)')
xlabel('Time')
ylabel('Amplitude')
% Discrete Plot
subplot(3,2,2)
stem(t,x)
title('Discrete => Duty cycle=25% and frequency=5Hz (801961005)')
xlabel('Time')
ylabel('Amplitude')
%-------- Case2: Duty cycle=50% and frequency=10Hz --------%
% Continous Plot
% Time
t = 1:0.01:10;
duty_cycle = 50;
freq = 10;
6|Page
Digital Signal Processing Lab
x = square(2*pi*freq*t,duty_cycle);
subplot(3,2,3)
plot(t,x)
title('Continous => Duty cycle=50% and frequency=10Hz (801961005)')
xlabel('Time')
ylabel('Amplitude')
% Discrete Plot
subplot(3,2,4)
stem(t,x)
title('Discrete => Duty cycle=50% and frequency=10Hz (801961005)')
xlabel('Time')
ylabel('Amplitude')
%-------- Case3: Duty cycle=75% and frequency=15Hz --------%
% Continous Plot
% Time
t = 1:0.01:10;
duty_cycle = 75;
freq = 15;
x = square(2*pi*freq*t,duty_cycle);
subplot(3,2,5)
plot(t,x)
title('Continous => Duty cycle=75% and frequency=15Hz (801961005)')
xlabel('Time')
ylabel('Amplitude')
% Discrete Plot
subplot(3,2,6)
stem(t,x)
title('Discrete => Duty cycle=75% and frequency=15Hz (801961005)')
xlabel('Time')
ylabel('Amplitude')
7|Page
Digital Signal Processing Lab
OUTPUT: Part 1 (b)
MATLAB CODE: Part 1 (c)
%%
close all
clear all
clc
% Case 1: f=0.8,A=100,Phase=90
% Time
t=0:0.001:10;
% Frequency
freq= 0.8;
% Amplitude
Amp = 100;
8|Page
Digital Signal Processing Lab
% Phase
phase = 90;
% sin wave
Out = Amp*sin(2*pi*freq*t);
%Plot
subplot(2,1,1)
plot(t,Out)
grid on
xlabel('Time')
ylabel('Output Signal')
title('Sinusoidal signal,f=0.8,A=100,Phase=90 (801961005)')
% Case 2: f=5,A=50,Phase=45
% Time
t=0:0.001:10;
% Frequency
freq= 5;
% Amplitude
Amp = 50;
% Phase
phase = 45;
% sin wave
Out = Amp*sin(2*pi*freq*t);
%Plot
subplot(2,1,2)
plot(t,Out)
grid on
title('Sinusoidal signal,f=5,A=50,Phase=45 (801961005)')
xlabel('Time')
ylabel('Output Signal')
9|Page
Digital Signal Processing Lab
OUTPUT: Part 1 (c)
10 | P a g e
Digital Signal Processing Lab
Experiment No-2
AIM:
Write a program
a) To determine N-point DFT of the user input sequence (without using built in command)
and plot its magnitude and phase spectrum.
b) Compare the IDFT of the results obtained in (a).
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE:
close all
clear all
clc
x = input('Enter the sequence for FFT = ');
N = length(x); %finding the length of entered sequence for N point FFT
for k = 1:N
y(k) = 0;
for n = 1:N
% FFT function
y(k) = y(k)+x(n)*exp(-i*2*pi*(k-1)*(n-1)/N);
end
end
t_value = 0:N-1;
subplot(2,2,1);
stem(t_value,x);
grid on;
ylabel('Amplitude');
xlabel('K');
title('Input Sequence (801961005)');
11 | P a g e
Digital Signal Processing Lab
% Magnitudes of individual FFT points
magnitude = abs(y);
subplot(2,2,2);
stem(t_value,magnitude);
grid on;
ylabel('Amplitude');
xlabel('n');
title('Magnitude (801961005)');
% Phase Plot
Phase_1 = angle(y);
disp(Phase_1);
subplot(2,2,3);
stem(t_value,Phase_1);
grid on;
ylabel('Phase');
xlabel('n');
title('Phase (801961005)');
% IDFT
L_new = length(y);
for n = 1:L_new
x_new(n) = 0;
for k = 1:L_new
x_new(n) = x_new(n)+(1/L_new)*y(k)*exp(1i*2*pi*(k-1)*(n-1)/L_new);
end
end
t_value = 0:L_new-1;
subplot(2,2,4);
stem(t_value,x_new);
ylabel('Amplitude');
xlabel('n');
12 | P a g e
Digital Signal Processing Lab
title('IFFT sequence (801961005)');
grid on;
OUTPUT:
13 | P a g e
Digital Signal Processing Lab
Experiment No-3
AIM: WAP to determine the Linear Convolution (without using inbuilt command) of any two
discrete sequences.
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE:
%% Linear Convolution
close all
clear all
clc
% num is the range of input variables
num = 15;
% Random variable
L=randi(10,1,num);
M= randi(10,1,num);
m =length(M);
n =length(L);
N = m+n-1;
M1=[L,zeros(1,m)];
L1=[M,zeros(1,n)];
% Linear Convolution without using in-built command
for i =1:N
y(i)=0;
for j=1:i
val = (i-j+1);
if(val>0)
y(i)=[y(i)+L1(j)*M1(val)];
14 | P a g e
Digital Signal Processing Lab
end
end
end
% Plot
subplot(2,1,1)
stem(y,'linewidth',2)
grid on
title('Linear Convolution (801961005)')
xlabel('n')
ylabel('Y(n)')
% Linear Convolution using in-built command
Out = conv(L,M);
subplot(2,1,2)
stem(Out,'linewidth',2)
grid on
title('Linear Convolution using in-built command (801961005)')
xlabel('n')
ylabel('Y(n)')
15 | P a g e
Digital Signal Processing Lab
OUTPUT:
16 | P a g e
Digital Signal Processing Lab
Experiment No-4
AIM: WAP to determine the Circular Convolution (without using inbuilt command) of user
defined two discrete sequences.
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE:
%% Circular Convolution
close all
clear all
clc
seq = input('Enter the sequence 1');
seq1 = input('Enter the sequence 2');
% num is the range of input variables
num = length(seq);
num1 = length(seq1);
% Random variable
L = seq;
M = seq1;
N = max(num,num1);
if num>num1
L1=[L,zeros(1,num1)];
M1=[M,zeros(1,num)];
else
L1=[L,zeros(1,num)];
M1=[M,zeros(1,num1)];
end
y = zeros(1,N);
% Circular Convolution without using in-built command
17 | P a g e
Digital Signal Processing Lab
for i =0:N-1
for j=0:N-1
val=mod(i-j,N);
y(i+1)=[y(i+1)+M1(j+1).*L1(val+1)];
end
end
% Plot
subplot(2,1,1)
stem(y,'linewidth',2)
grid on
title('Circular Convolution (801961005)')
xlabel('n')
ylabel('Y(n)')
% Circular Convolution using in-built command
Out = cconv(M,L,N);
subplot(2,1,2)
stem(Out,'linewidth',2)
grid on
title('Circular Convolution using in-built command(801961005)')
xlabel('n')
ylabel('Y(n)')
18 | P a g e
Digital Signal Processing Lab
OUTPUT:
19 | P a g e
Digital Signal Processing Lab
Experiment No-5
AIM: For any two-user input discrete sequence compute circular convolution using DFT-IDFT
method (without inbuilt command).
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE:
%% Circular Convolution
close all
clear all
clc
%circular convolution using DFT-IDFT (without inbuilt command)
xn=input('enter sequence 1=');
hn=input('enter sequence 2=');
L1=length(xn);
L2=length(hn);
N=max(L1,L2);
xn=[xn,zeros(1,N-L1)];
hn=[hn,zeros(1,N-L2)];
y=zeros(1,N);
F=fft(xn,N);
J=fft(hn,N);
Q=F.*J;
I=ifft(Q)
subplot(2,1,1)
stem(I);
title('circular convolution using DFT-IDFT(without inbuilt command)’)
xlabel('n')
ylabel('y(n)')
20 | P a g e
Digital Signal Processing Lab
%Circular convolution with inbuilt command
out=cconv(xn,hn,N);
subplot(2,1,2)
stem(out)
title('circular convolution with inbuilt command(801961005)')
xlabel('n')
ylabel('y(n)')
OUTPUT:
21 | P a g e
Digital Signal Processing Lab
Experiment No-6
AIM: Write a program to determine time domain and frequency domain response of fixed
windows by taking N=25.
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE:
%% Windows
close all
clear all
clc
% Hamming Window
N = 25;
for n = 0:N
w(n+1) = 0.54 - 0.46*cos(2*pi*n/(N));
end
subplot(421)
plot(0:N,w,'linewidth',1)
xlabel('Samples')
ylabel('Amplitude')
title('Hamming--Time Domain Plot')
grid on
[t,f1] = freqz(w);
t1 = abs(t);
subplot(422)
plot(f1/pi,10*log(t1),'linewidth',1)
xlabel('Normalized Frequency')
ylabel('Magnitude[dB]')
title('Hamming--Frequency Domain Plot')
22 | P a g e
Digital Signal Processing Lab
grid on
clear all
% Hanning Window
N = 25;
for n = 0:N
w(n+1) = 0.5 - 0.5*cos(2*pi*n/(N));
end
subplot(423)
plot(0:N,w,'linewidth',1)
xlabel('Samples')
ylabel('Amplitude')
title('Hanning--Time Domain Plot')
grid on
[t,f1] = freqz(w);
t1 = abs(t);
subplot(424)
plot(f1/pi,10*log(t1),'linewidth',1)
xlabel('Normalized Frequency')
ylabel('Magnitude[dB]')
title('Hanning--Frequency Domain Plot')
grid on
clear all
% Rectangular Window
N = 25;
for n = 0:N
w(n+1) = 1;
end
subplot(425)
plot(0:N,w,'linewidth',1)
xlabel('Samples')
23 | P a g e
Digital Signal Processing Lab
ylabel('Amplitude')
title('Rectangular--Time Domain Plot')
grid on
[t,f1] = freqz(w);
t1 = abs(t);
subplot(426)
plot(f1/pi,10*log(t1),'linewidth',1)
xlabel('Normalized Frequency')
ylabel('Magnitude[dB]')
title('Rectangular--Frequency Domain Plot')
grid on
clear all
% Blackman Window
N = 25;
for n = 0:N
w(n+1) = 0.42 - 0.5*cos(2*pi*n/N)+ 0.08*cos(4*pi*n/N);
end
subplot(427)
plot(0:N,w,'linewidth',1)
xlabel('Samples')
ylabel('Amplitude')
title('Blackman--Time Domain Plot')
grid on
[t,f1] = freqz(w);
t1 = abs(t);
subplot(428)
plot(f1/pi,10*log(t1),'linewidth',1)
xlabel('Normalized Frequency')
ylabel('Magnitude[dB]')
title('Blackman--Frequency Domain Plot')
24 | P a g e
Digital Signal Processing Lab
OUTPUT:
25 | P a g e
Digital Signal Processing Lab
Experiment No-7
AIM: Design FIR low pass filter using window parameters which includes Pass band Edge
frequency, Sampling frequency, Transition Width, and Stop Band Attenuation.
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE:
%%
close all
clear all
clc
fp = 1500;
fs = 800;
tw = 500;
fs_att = 19;
fp1 = fp/fs;
tw1 = tw/fs;
fc = fp1+ tw1/2;
% N = round(0.9/tw1);
N = 40;
n = (-(N-1)/2):(N-1)/2;
rectangular = [ones(1,N)];
h = [ones(1,N)];
hd = [ones(1,N)];
for i = 1:N
wc = 2*pi*fc;
h(i) = 2*fc*sin(n(i)*wc)/(n(i)*wc);
hd(i) = h(i)*rectangular(i);
end
subplot(121);
stem(n,hd);
title('LPF with RECTANGULAR WINDOW');
xlabel('n');
ylabel('Filter Coeff.h');
[X2,w2] = freqz(hd,1,1024);
% X2 = fftshift(X2);
26 | P a g e
Digital Signal Processing Lab
subplot(122);
plot(w2/(2*pi),20*log10(abs(X2)/max(X2)));
title('LPF with RECTANGULAR WINDOW Frequency Response');
xlabel('Normalised f');
ylabel('Norm.Magnitude Resp.(dB)');
OUTPUT:
27 | P a g e
Digital Signal Processing Lab
Experiment No-8
AIM: Write a program to perform the decimation without using in-built function.
SOFTWARE REQUIRED:
MATLAB R2016a
MATLAB CODE:
%%
close all
clear all
clc
n = 0:50;
x = sin(n);
h = fir1(128-1,1/3);
xf = filter(h,1,x);
yf = downsample(xf,3);
ynf = downsample(x,3);
f = -1:1/512:1;
X = freqz(x,1,2*pi*f);
Xf = freqz(xf,1,2*pi*f);
Yf = freqz(yf,1,2*pi*f);
Ynf = freqz(ynf,1,2*pi*f);
subplot(411)
plot(f,abs(X))
title('Unfiltered Input')
subplot(412)
plot(f,abs(Ynf))
title('Down by 3 w/o Filter Output (Showing Aliasing)')
subplot(413)
plot(f,abs(Xf))
28 | P a g e
Digital Signal Processing Lab
title('Filtered Input')
subplot(414)
plot(f,abs(Yf))
title('Down by 3 with Filter Output')
OUTPUT:
29 | P a g e