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.

CreatedDec 10, 2019

UpdatedDec 10, 2019

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Introduction
Basic operations on Matrices
Genaration of various signals and sequences
Operations on signals and sequences
Finding the even and odd parts of signal/sequence and real and imaginary parts of signal
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
Finding the Fourier transform of a given signal and plotting its magnitude and phase spectrum
Laplace Transforms
Locating the zeros and poles and plotting the pole zero maps in zplane for the given transfer function
Gaussian Noise
Verification of Wiener Khinchin relation
Removal of noise by autocorrelation/crosscorrelation
Extraction of Periodic signal masked by noise using correlation.
Checking a Random process for stationarity in wide sense
To find a mean and variance of a discrete random variable
To find a moment generating function of a discrete random variable
Computation of Energy of sinusoidal signal
Computation of energy of rectangular pulse
Computation of Average Power
Waveform Synthesis
Find and plot the cumulative distribution and probability density functions of a random variable
Verification of central limit theorem