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.
Printer Support
BalasHapushp printer customer care number
samsung printer support number
Epson Printer Support Number
Canon Printer Support Number
Brothers Printer Support Number
Best Digital Marketing Company in India
This is a great post. I like this topic.This site has lots of advantage.I found many interesting things from this site. It helps me in many ways.Thanks for posting this again.
BalasHapusaol email technical support number
att email customer support number
roadrunner email support
Yahoo email support number