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 autocorrelation function of a widesensestationary 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 distortionless 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 PaleyWiner 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.

UpdatedDec 10, 2019

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