Spectrum and spectral density estimation by the Discrete Fourier transform

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Spectrum and spectral density estimation by the Discrete Fouriertransform (DFT), including a comprehensive list of windowfunctions and some new flat-top windows.

This report tries to give a practical overview about the estimation of power spectra/powerspectral densities using the DFT/FFT. One point that is emphasized is the relationship between estimates of power spectra and power spectral densities which is given by the effectivenoise bandwidth (ENBW). Included is a detailed list of common and useful window functions, among them the often neglected flat-top windows. Special highlights are a procedureto test new programs, a table of comprehensive graphs for each window and the introductionof a whole family of new flat-top windows that feature sidelobe suppression levels of upto −248 dB, as compared with −90 dB of the best flat-top windows available until now.

https://holometer.fnal.gov/GH_FFT.pdf