# How is the PowerSpectralDensity function implemented? [closed]

I am working on a signal processing lecture for undergraduate students with Mathematica exercises/examples, and I would like to explain to them what happens when they run the PowerSpectralDensity[data,...] function. It returns a linear combination of cosines, so I suspect that maybe a linear regression is used behind the scenes (which is one of the well-known ways of constructing periodograms), but it would be nice to know for sure. Any hints would be much appreciated.

• Have you looked at the Details and Options of PowerSpectralDensity? – corey979 Apr 12 '19 at 11:25
• Voting to close as "easily found in documentation", as it seems to be explained there. If you disagree, please clarify. – Szabolcs Apr 12 '19 at 11:43
• Generally, for "how does it work" questions, I suggest the following steps (in order): 1. Check the function's documentation page. Always check carefully under the Details and in the Background section. 2. See if there are advanced tutorials (always check the Related Tutorials and do an additional search) E.g. NDSolve, NDSolve and GraphPlot have advanced tutorials which detail the methods they use 3. Check here: reference.wolfram.com/language/tutorial/… 4. Search StackExchange 5. If still no luck, write to Wolfram Support – Szabolcs Apr 12 '19 at 11:46
• @corey979 Yes, I did check the "Details and Options". Looks like they Fourier-transform the empirical covariance function, Wiener-Khinchin-theorem-style. Which is bad for my lecture because I want to introduce that topic "independently". – Laryx Decidua Apr 12 '19 at 13:35