Periodogram PSD vs FFT PSD

When power scaling the magnitude of the output from an FFT one could use the following scaling which equivocates the psd of the FFT to the MSE of the time series:

PSD0=(abs(x)/N)^2

PDSi=2*(abs(x)/N)^2 for i=1, 2, …n/2+1

The MatLab function ‘periodogram’ returns PSD values that sum to twice the MSE of the time series (each PSD value is twice the FFT value). Why is that? Both analysis were done with no windowing.

[Honglei Chen]

Hi Terry, could you show the comparison code?