# What is the difference between the functions PSD and PWELCH?

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MathWorks Support Team on 27 Jun 2009
Edited: Lisa Justin on 10 Oct 2017
Both of these functions use Welch's method to estimate the PSD.

MathWorks Support Team on 27 Jun 2009
We highly recommend that you use PWELCH for Welch's method of estimation rather than PSD. Although PSD was an implementation of Welch's method, PWELCH was added for the following reasons:
The name of the function PWELCH reflects much better the method used to obtain the spectral estimate. PSD is too generic, in fact there are several different algorithms for psd estimation.
Also, PSD does not scale the data by a factor of Fs (sampling frequency). Thus, PSD was actually more of a power spectrum estimate (yielding units of power or db) whereas PWELCH and our other functions return a power spectral density estimate (yielding units of power/freq or db/freq).
The units are of importance because a density (from PWELCH) can be integrated to obtain an estimate of the average power over a given frequency interval. When you integrate you will get units of power not power/freq.
Moreover, PWELCH returns a single sided spectrum by default (for real signals). This means that the total power of the signal is contained in half the spectrum [0 to Fs/2]. In other words, if you integrate the single-sided PSD estimate from [0 to Fs/2], you will get the average power estimate over the entire Nyquist interval. You will get the same result of integrating the double-sided PSD estimate over the interval [-Fs/2 Fs/2].

#### 1 Comment

Lisa Justin on 10 Oct 2017
Do you mean that the PSD function is a Power Spectrum estimate rather than a PSD estimate? Are there any overlaps with PSD?

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