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PSD vs FFT Magnitude squared

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arve9066

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Suppose my time-domain signal is a voltage signal. I sample this at the correct rate, and taking the Fourier transform gives me the magnitudes of of various frequency components present in the signal (within the context of sampling rate). Taking the modulus squared of this quantity will give me power/Hz, right?

Taking the Fourier transform of the autocorrelation function (rather than the direct transform as discussed earlier) gives the PSD in power/Hz

What is the difference between these two? if both have units of power/Hz, why/when should I do one over the other?
 

Depending upon the available processing resources and memory, there are different types of optimizations available for either method.
Back before the days of multi-GHz CPUs and Gigabytes of memory, these were major constraints. Less so now.
You may also find it interesting to look that the Hartley transform (real value in -> real value out) and its usefulness in calculating power spectral density.
 

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