MATLAB: Why is periodogram(y,w) not periodogram(y.*w)

Question

why is periodogram(y,w) not the same as periodogram(y.*w), where y is the signal and w the window. For a rectangular window it is the same but for a hanning window there is a difference that has something to do with the mean and variance of the window I guess. What exactly is this difference? And why is this difference there? Same holds for pwelch.

Answer 1

The difference is that the syntax periodogram(y,w) uses the window normalization constant explained here:

http://www.mathworks.com/help/signal/ug/spectral-analysis.html#f12-20709

Read about the modified periodogram.

While periodogram(y.*w) does not use that normalization because you are using a rectangular window

I would recommend using

periodogram(y,w)

However, if you look at the two periodograms, you'll see that one is simply a scaled version of the other and that scaling is due to window normalization you get with

periodogram(y,w)