The averaged periodogram addresses the limitations of the periodogram by using averaging to reduce variance. Use of averaging to reduce variance is a common theme in many nonparametric spectrum estimators. In this lesson you will learn how the averaged periodogram estimates the power spectral density. You will also learn how choices for window, segment length, and overlap affect the performance of the estimator. This knowledge will enable you to perform spectrum estimation and provides a starting point for understanding other nonparametric methods.

## Prerequisites

## Video

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Raghu Ram says

Dear Barry,

I want to estimate power spectral density of a signal. I used matlab inbuilt function called pwelch. I am getting different magnitude for these function

1. [Pxx,F] = PWELCH(X,WINDOW,NOVERLAP,F,Fs)

2. [Pxx,W] = PWELCH(X,WINDOW,NOVERLAP,W).

I want to represent figure dB Vs Frequency.

In case of first function the magnitude is achieved 10dB and -50dB for second function. Please can you explain what is the reason changes in magnitude when we change angular frequency (w) to normal frequency (f) .

Barry Van Veen says

I am 99% sure that the difference in magnitude is a result of pwelch calculating the power spectral DENSITY. In case 2 the spectrum is normalized with respect to the interval [0,pi] radians (assuming your data is real), while in case 1 it is normalized with respect to the interval [0,Fs/2] Hz. That is, in one case the units are Watts/radian while in the other they are Watts/Hz. The amplitude typically is normalized so that the total area under the power spectral density is equal to the variance of the data. Hence, different units result in different amplitudes. I can't tell for sure whether this is what you are running into, but I strongly suspect that is the case.