ESTIMATION OF PERIODOGRAM

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    ESTIMATION OF PERIODOGRAM

    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.




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