ESTIMATION OF PERIODOGRAM
AIM
To estimate the power spectral density of a given signal using periodogram
in MATLAB.
THEORY
The power spectral density (PSD) of a WSS process is the Fourier transform of the autocorrelation sequence. Periodogram is a non-parametric method to estimate PSD
() = (k)
For an autocorrelation ergodic process and an unlimited amount of data, the autocorrelation sequence may be detemined by using the time average
(k) = (n+k)x*(n)
If x(n) is only measured over a finite interval, say n=1,2,…N-1, then the autocorrelation sequence must be estimated using with a finite sum
(r) = () (n+k)x*(n)
In order to ensure that the value of x(n) that is fully outside the interval [0,N-1] are excluded and written as follows
(k) = () (n+k)x*(n) k=0,1,2….,N-1.
Taking the discrete Fourier transform of rx^(k) leads to an estimation of the power spectrum known as the periodogram.
() = (k)
The periodogram
() = ()() = ()
Where XN(ejw) is the discrete time Fourirer transform of the N-point data sequence XN(n)
() = (n) =
ALGORITHM
STEP 1: Compute the value of x.
STEP 2: Perform periodogram function for x signal.
STEP 3: Using pwelch function, smoothen the output of periodogram signal.
STEP 4: Plot the graph for input and output signal
PROGRAM
##########################################################
clc;
clear all;
close all;
fs=1000;
t=0.1:1/fs:0.3;
x=cos(2*pi*t*200)+0.1*randn(size(t));
figure(1);
plot(x);
title('input signal');
xlabel('time');
ylabel('amplitude');
figure(2);
periodogram(x,[],'one sided',512,fs);
figure(3);
pwelch(x,30,10,[],fs,'one sided');
#############################################################
RESULT
Thus the MATLAB program to estimate the power spectral density of given signal using periodogram is executed and output is plotted.
BalasHapuspug puppies for sale,pug puppies for sale near me
teacup pugs for sale,teacup pugs,teacup pug puppies for sale,teacup pug for sale near me,pug for sale near me,pug puppies for sale under,teacup pugs,pug puppies near me,teacup pugs,teacup pug puppies for sale,pug puppy for sale,mini pug,baby pugs for sale,pug breeders near me,pugs puppies for sale,black pug puppies for sale,miniature pug,pug puppies,pugs for sale near me,pugs for sale near me,pugs puppies,teacup pug puppies for sale,pugs for sale,baby pugs for sale
Pug pupies for sale
pug puppies for sale near me
pug puppy for sale near me
teacup puppies for sale near me
Pug puppies for sale
pugs for sale
french bulldog puppies for sale
French Bulldog Puppy for sale near me