Question

write a computer program to find the auto-correlation of any energy signal and to find its energy spectral density.

test your program the signal : tri(t/2).

Answer #1

MATLABCODE:

clc;

close all;

clear all;

T = -1:0.1:1; % Time vector

W = 1; % width of the triangulat pulse

tri = tripuls(T,W) ;

figure;plot(T,tri);grid;title('Energy signal: Triangular
pulse');

Acorr = autocorr(tri);

figure;plot(T,Acorr);grid;title('Autocorrelation of Triangular
pulse');

% Now take fourier transform of autocorrelation function

% For power spectral density

Fs = 10; % Sampling frequency

T = 1/Fs; % Sampling period

L = length(Acorr); % Length of signal

t = (0:L-1)T; % Time vector

Y = fft(Acorr);

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2P1(2:end-1);

f = Fs*(0:(L/2))/L;

figure; plot(f,P1) ;grid;

title('Single-Sided Power Spectrum ')

xlabel('f (Hz)')

ylabel('|P1(f)|')

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