# Verification of Wiener- Khinchin relation

AIM: verification of wiener–khinchin relation

EQUIPMENT:

PC with windows (95/98/XP/NT/2000).

MATLAB Software

Theory:  It states that the auto-correlation function of a wide-sense-stationary random process has a spectral decomposition given by the power spectrum of that process.

Program:

clc

clear all;

t=0:0.1:2*pi;

x=sin(2*t);

subplot(3,2,1);

plot(x);

au=xcorr(x,x);

subplot(3,2,2);

plot(au);

v=fft(au);

subplot(3,2,3);

plot(abs(v));

fw=fft(x);

subplot(3,2,4);

plot(fw);

fw2=(abs(fw)).^2;

subplot(3,2,5);

plot(fw2);

Output:

Result: The wiener–khinchin relation is verified.

Viva Questions:

1. Define Gibbs Phenomena

Ans: The Gibbs phenomenon involves both the fact that Fourier sums overshoot at a jump discontinuity, and that this overshoot does not die out as the frequency increases.

2. Define the condition for distortion less transmission through the system

Ans:  Transmission is said to be distortion less if the input and output have identical wave shapes within a multiplicative constant.A delayed output that retains the input waveform is also considered distortion less.Thus in distortion-less transmission, the input x(t) and output y(t) satisfy the condition:

y(t) = Kx(t - t) where t is the delay time and k is a constant

3. What is Paley-Winer criterion?

Ans:  Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform.

4.What is frequency response?

Ans: Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input.

• Created
Dec 10, 2019
• Updated
Dec 10, 2019
• Views
714
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