correlation between two signals and sequences

CORRELATION:

The concept correlation can be defined as similarities of two waveforms. It may determine if signal x₁(t) waveform contain an amount c₂x₂(t) of that particular waveform x₂(t) in the interval of (t₁, t₂). It is a measure of the degree to which two sequences are similar.Correlation is of two types cross correlation and autocorrelation.

Cross correlation:

Cross-correlation between two signals indicates what proportion one signal is said to the time-delayed version of another signal.

clc;

close all;

clear all;

% two input sequences

x=input(‘enter input sequence’);

h=input(‘enter the impulse sequence’);

subplot(2,2,1);

stem(x);

xlabel(‘n’);

ylabel(‘x(n)’);

title(‘input sequence’);

subplot(2,2,2);

stem(h);

xlabel(‘n’);

ylabel(‘h(n)’);

title(‘impulse sequence’);

% cross correlation between two sequences

y=xcorr(x,h);

subplot(2,2,3);

stem(y);

xlabel(‘n’);

ylabel(‘y(n)’);

title(‘ cross correlation between two sequences ‘);

Autocorrelation:

The auto correlation function is a special form of cross correlation function.

clc;

close all;

clear all;

% two input sequences

x=input(‘enter input sequence’);

h=input(‘enter the impulse sequence’);

subplot(2,2,1);

stem(x);

xlabel(‘n’);

ylabel(‘x(n)’);

title(‘input sequence’);

subplot(2,2,2);

stem(h);

xlabel(‘n’);

ylabel(‘h(n)’);

title(‘impulse sequence’);

% auto correlation of input sequence

z=xcorr(x,x);

subplot(2,2,4);

stem(z);

xlabel(‘n’);

ylabel(‘z(n)’);

title(‘auto correlation of input sequence’);

crosscorrelation between two signals

clc;

close all;

clear all;

% cross correlation between two signals

% generating two input signals

t=0:0.2:10;

x1=3*exp(-2*t);

h1=exp(t);

figure;

subplot(2,2,1);

plot(t,x1);

xlabel(‘t’);

ylabel(‘x1(t)’);

title(‘input signal’);

subplot(2,2,2);

plot(t,h1);

xlabel(‘t’);

ylabel(‘h1(t)’);

title(‘impulse signal’);

% cross correlation

subplot(2,2,3);

z1=xcorr(x1,h1);

plot(z1);

xlabel(‘t’);

ylabel(‘z1(t)’);

title(‘cross correlation ‘);

% auto correlation

subplot(2,2,4);

z2=xcorr(x1,x1);

plot(z2);

xlabel(‘t’);

ylabel(‘z2(t)’);

title(‘auto correlation ‘);