Finding the even and odd parts of signal/sequence and real and imaginary parts of signal
Aim: Program for finding even and odd parts of signals Using MATLAB Software.
Equipments:
PC with windows (95/98/XP/NT/2000).
MATLAB Software.
1. Even and odd parts of signal program:
close all;
clear all;
t=0:.005:4*pi;
x=sin(t)+cos(t); % x(t)=sint(t)+cos(t)
subplot(2,2,1)
plot(t,x)
xlabel('t');
ylabel('amplitude')
title('input signal')
y=sin(-t)+cos(-t) % y=x(-t)
subplot(2,2,2)
plot(t,y)
xlabel('t');
ylabel('amplitude')
title('input signal with t=-t')
z=x+y
subplot(2,2,3)
plot(t,z/2)
xlabel('t');
ylabel('amplitude')
title('even part of the signal')
p=x-y
subplot(2,2,4)
plot(t,p/2)
xlabel('t');
ylabel('amplitude')
title('odd part of the signal')

2. Even and odd parts of signal program:
%finding Odd and even parts of a signal
clc
clear all
close all
f=input('enter frequency')
T=1/f;
t=0:T/f:T
x=sin(2*pi*f*t)
t1=-fliplr(t)
t1(length(t1))=[]
t2=[t1 t]
x1=zeros(1,length(t2))
i=find(t2==min(t))
x1(i:length(x1))=x
y=fliplr(x1)
xe=(x1+y)*0.5
xo=(x1-y)*0.5
subplot(2,2,1)
plot(t,x)
title('input sequence')
xlabel('time')
ylabel('amplitude')
subplot(2,2,2)
plot(t2,xo)
title('odd part of sequence')
xlabel('time')
ylabel('amplitude')
subplot(2,2,3)
plot(t2,xe)
title('even part of sequence')
xlabel('time')
ylabel('amplitude')
Output:

1.Even and odd parts of sequence program:
t=-4:1:4;
h=[ 2 1 1 2 0 1 2 2 3 ];
subplot(3,2,1)
stem(t,h);
xlabel('time'); ylabel('amplitude');
title('signal');
n=9;
for i=1:9
x1(i)=h(n);
n=n-1;
end
subplot(3,2,2)
stem(t,x1);
xlabel('time'); ylabel('amplitude');
title('folded signal');
z=h+x1
subplot(3,2,3);
stem(t,z);
xlabel('time'); ylabel('amplitude');
title('sum of two signal');
subplot(3,2,4);
stem(t,z/2);
xlabel('time'); ylabel('amplitude');
title('even signal');
a=h-x1;
subplot(3,2,5);
stem(t,a);
xlabel('time'); ylabel('amplitude');
title('difference of two signal');
subplot(3,2,6);
stem(t,a/2);
xlabel('time'); ylabel('amplitude');
title('odd signal');

2.Even and odd parts of sequence program:
clc
clear all
close all
x=[1 2 3]
n=[0 1 3]
n1=-fliplr(n)
n1(length(n1))=[]
n2=[n1 n]
x1=zeros(1,length(n2))
i=find(n2==min(n))
x1(i:length(x1))=x
y=fliplr(x1)
xe=(x1+y)*0.5
xo=(x1-y)*0.5
subplot(2,2,1)
stem(n,x)
title('input sequence')
xlabel('time')
ylabel('amplitude')
subplot(2,2,2)
stem(n2,xo)
title('odd part of sequence')
xlabel('time')
ylabel('amplitude')
subplot(2,2,3)
stem(n2,xe)
title('even part of sequence')
xlabel('time')
ylabel('amplitude')
Output:

ENERGY AND POWER SIGNAL: A signal can be categorized into energy signal or power signal:
Energy signal has a finite energy, 0 < E < 8. And Power=0
Energy signals have values only in the limited time duration.
Example: A signal having only one square pulse is energy signal.
A signal that decays exponentially has finite energy
Energy of Continuous Signals

Energy of Discrete Signals

Power signal has a finite energy, 0 < P < 8. And Energy =8
Example: sine
Power of Continuous Signals

Power of Discrete Signals

% Program to find the energy of signal
clc;
close all;
clear all;
x=[1,2,3];
n=3
e=0;
for i=1:n;
e=e+(x(i).*x(i));
end
% Program to find the energy of signal
clc;
close all;
clear all;
N=2
x=ones(1,N)
for i=1:N
y(i)=(1/3)^i.*x(i);
end
n=N;
e=0;
for i=1:n;
e=e+(y(i).*y(i));
end
% Program to find the power of signal
clc;
close all;
clear all;
N=2
x=ones(1,N)
for i=1:N
y(i)=(1/3)^i.*x(i);
end
n=N;
e=0;
for i=1:n;
e=e+(y(i).*y(i));
end
p=e/(2*N+1);
% Program to find the power of signal
N=input('type a value for N');
t=-N:0.0001:N;
x=cos(2*pi*50*t).^2;
disp('the calculated power p of the signal is');
P=sum(abs(x).^2)/length(x)
plot(t,x);
axis([0 0.1 0 1]);
disp('the theoretical power of the signal is');
Output: P_theory=3/8
Result:
The even and odd parts of signal/sequence and real and imaginary part of signals are calculated and plotted.
-
CreatedDec 02, 2019
-
UpdatedMar 01, 2020
-
Views865
Introduction
Basic operations on Matrices
Genaration of various signals and sequences
Operations on signals and sequences
Finding the even and odd parts of signal/sequence and real and imaginary parts of signal
Verification of Linearity and time in-variance properties of a given continuous/discrete system
Linear Convolution
Auto correlation and cross correlation between signals and sequences
Computation of unit sample, unit step and sinusoidal response of the given LTI system and verifying its physical reliability and stability properties
GIBBS phenomenon
Sampling theorem verification
Finding the Fourier transform of a given signal and plotting its magnitude and phase spectrum
Laplace Transforms
Locating the zeros and poles and plotting the pole zero maps in z-plane for the given transfer function
Gaussian Noise
Verification of Wiener- Khinchin relation
Removal of noise by auto-correlation/cross-correlation
Extraction of Periodic signal masked by noise using correlation.
Checking a Random process for stationarity in wide sense
To find a mean and variance of a discrete random variable
To find a moment generating function of a discrete random variable
Computation of Energy of sinusoidal signal
Computation of energy of rectangular pulse
Computation of Average Power
Waveform Synthesis
Find and plot the cumulative distribution and probability density functions of a random variable
Verification of central limit theorem