Checking a Random process for stationarity in wide sense
AIM: Checking a random process for stationarity in wide sense.
EQUIPMENTS:
PC with windows (95/98/XP/NT/2000).
MATLAB Software
Theory: A stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space. As a result, parameters such as the mean and variance. If they exist, also do not change over time or position.
MATLAB PROGRAM:
clear all
clc
y = randn([1 40])
my=round(mean(y));
z=randn([1 40])
mz=round(mean(z));
vy=round(var(y));
vz=round(var(z));
t = sym('t','real');
h0=3;
x=y.*sin(h0*t)+z.*cos(h0*t);
mx=round(mean(x));
k=2;
xk=y.*sin(h0*(t+k))+z.*cos(h0*(t+k));
x1=sin(h0*t)*sin(h0*(t+k));
x2=cos(h0*t)*cos(h0*(t+k));
c=vy*x1+vz*x1;
%if we solve "c=2*sin(3*t)*sin(3*t+6)" we get c=2cos(6)
%which is a constant does not depend on variable 't'
% so it is wide sense stationary
CONCLUSION: In this experiment the checking a random process for stationary in wide sense have been verified using MATLAB
VIVA QUESTIONS
1. Define Signal.
Ans: Signal is function of one or more variables to convey information.
2. Define deterministic and Random Signal.
Signal that can be modeled exactly by a mathematical formula is known as deterministic signal.Random signals are random variables which evolve, often with time (e.g. audio noise), but also with distance (e.g. intensity in an image of a random texture), or sometimes another parameter.

CreatedFeb 02, 2020

UpdatedFeb 02, 2020

Views270
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