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I am working on a project and came across a conceptual roadblock.

I am working with a PSD, lets say the units are V^2/Hz.

I choose a dF based on how many sine tones I want in the time signal I am going to create.

I sample the PSD curve at my frequency bin locations; so I have both my frequency vector (0:dF:fMax) and my PSD sampled at each frequency bin.

I multiply my sampled PSD by dF, then take square root of each bin to get a amplitude spectrum. I add a phase to each amplitude bin, and modify my resulting spectrum (amplitude+phase) so that it has Hermitian Symmetry.

IFFT, results in a purely real time signal.

All makes sense up till here.

Now, if I take this tiem frame and concatonate it with itself, I get a frame twice as big. If I FFT that 2x frame, I get a resulting FFT in which the magnitude of every other bin is 0 - which makes sense since the time signal wasn't generated with any of the 0-magnitude frequencies.

But, if I convert this FFT to a PSD, I will still see that every other point is 0 value.

This is my confusion - I thought that every PSD should be the same, regardless of what your sampling parameters are. It makes sense to me why every other bin is zero - but what bit of logic am I overlooking that would predict that my PSD will not match when sampled with 2N points? I thought PSDs were supposed to deal with the problem of sampling using different dFs.

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# Power Spectral Density Confusion

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