Removal of noise by autocorrelation/crosscorrelation
Aim: To verify the removal of noise by auto correlation/cross correlation.
EQUIPMENT:
PC with windows (95/98/XP/NT/2000).
MATLAB Software.
Theory:
Detection of a periodic signal masked by random noise is of great importance .The noise signal encountered in practice is a signal with random amplitude variations. A signal is uncorrelated with any periodic signal. If s(t) is a periodic signal and n(t) is a noise signal then
Qsn(T)= cross correlation function of s(t) and n(t) Then Qsn(T)=0
Detection of noise by AutoCorrelation:
S(t)=Periodic Signal (Transmitted) , mixed with a noise signal n(t).
Then f(t) is received signal is [s(t ) + n(t) ]
Let Qff(T) =Auto Correlation Function of f(t)
Qss(t) = Auto Correlation Function of S(t)
Qnn(T) = Auto Correlation Function of n(t)
The periodic signal s(t) and noise signal n(t) are uncorrelated
The Auto correlation function of a periodic signal is periodic of the same frequency and the Auto correlation function of a non periodic signal is tends to zero for large value of T since s(t) is a periodic signal and n(t) is non periodic signal so Qss(T) is a periodic where as aQnn(T) becomes small for large values of T Therefore for sufficiently large values of T Qff(T) is equal to Qss(T).
Detection by Cross Correlation:
f(t)=s(t)+n(t)
c(t)=Locally generated signal with same frequency as that of S(t)
T/2
Qfc (t) = Lim 1/T ? [s(t)+n(t)] [ c(tT)] dt
T8 T/2
= Qsc(T)+Qnc(T)
C(t) is periodic function and uncorrelated with the random noise signal n(t). Hence Qnc(T0=0) Therefore Qfc(T)=Qsc(T).
Applications:detection of radar and sonal signals ,detection of cyclical component in brain analysis meterology etc.
Program1 : auto correlation
clear all
clc
t=0:0.1:pi*4;
s=sin(t);
k=2;
subplot(6,1,1)
plot(s);
title('signal s');
xlabel('t');
ylabel('amplitude');
n = randn([1 126]);
f=s+n;
subplot(6,1,2)
plot(f);
title('signal f=s+n');
xlabel('t');
ylabel('amplitude');
as=xcorr(s,s);
subplot(6,1,3)
plot(as);
title('auto correlation of s');
xlabel('t');
ylabel('amplitude');
an=xcorr(n,n);
subplot(6,1,4)
plot(an);
title('auto correlation of n');
xlabel('t');
ylabel('amplitude');
cff=xcorr(f,f);
subplot(6,1,5)
plot(cff);
title('auto correlation of f');
xlabel('t');
ylabel('amplitude');
hh=as+an;
subplot(6,1,6)
plot(hh);
title('addition of as+an');
xlabel('t');
ylabel('amplitude');
Output:
Program2: CROSS CORRELATION :
clear all
clc
t=0:0.1:pi*4;
s=sin(t);
k=2;
%sk=sin(t+k);
subplot(7,1,1)
plot(s);
title('signal s');xlabel('t');ylabel('amplitude');
c=cos(t);
subplot(7,1,2)
plot(c);
title('signal c');xlabel('t');ylabel('amplitude');
n = randn([1 126]);
f=s+n;
subplot(7,1,3)
plot(f);
title('signal f=s+n');xlabel('t');ylabel('amplitude');
asc=xcorr(s,c);
subplot(7,1,4)
plot(asc);
title(' correlation of s and c');xlabel('t');ylabel('amplitude');
anc=xcorr(n,c);
subplot(7,1,5)
plot(anc);
title(' correlation of n and c');xlabel('t');ylabel('amplitude');
cfc=xcorr(f,c);
subplot(7,1,6)
plot(cfc);
title(' correlation of f and c');xlabel('t');ylabel('amplitude');
hh=asc+anc;
subplot(7,1,7)
plot(hh);
title('addition of sc+nc');xlabel('t');ylabel('amplitude');
Output:
Result: In this experiment the removal of noise by auto correlation/cross correlation have been verified using MATLAB.

CreatedDec 10, 2019

UpdatedDec 10, 2019

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Genaration of various signals and sequences
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Verification of Linearity and time invariance 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
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Laplace Transforms
Locating the zeros and poles and plotting the pole zero maps in zplane for the given transfer function
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Removal of noise by autocorrelation/crosscorrelation
Extraction of Periodic signal masked by noise using correlation.
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Verification of central limit theorem