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Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new flat-top windows. G. Heinzel ∗ , A. R¨ udiger and R. Schilling, Max-Planck-Institut f¨ ur Gravitationsphysik (Albert-Einstein-Institut) Teilinstitut Hannover February 15, 2002 Abstract This report tries to give a practical overview about the estimation of power spectra/power spectral densities using the DFT/FFT. One point that is emphasized is the relationship be- tween estimates of power spectra and power spectral densities which is given by the effective noise 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 procedure to test new programs, a table of comprehensive graphs for each window and the introduction of a whole family of new flat-top windows that feature sidelobe suppression levels of up to −248 dB, as compare d with −90 dB of the best flat-to p windows av ailabl e until now. Contents 1 Abbr evia tion s an d sy mbols 4 2 Pre face 5 3 In trod uc tio n 5 4 Sc ali ng bits to V ol ts 7 5 Discrete Fourier Transforma tion (DFT) 7 6 Some common uni ts 9 6.1 p eak, peak-peak and rms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6.2 decibel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 7 Sampli ng time, frequenc y bins etc . 10 ∗ e-mail: [email protected] 1

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