Spectrum and spectral density estimation by the Discrete Fourier transform (DFT, FFT), including a comprehensive list of window functions and some new flat-top windows

Document #:

LIGO-T1400010-v1

Document type:

T - Technical notes

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 func- tions, 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 compared with −90 dB of the best flat-top windows available until now.
(Note: Added by Josh Smith with permission from G. Heinzel - contact G. Heinzel for updated versions).

Files in Document:

• FFTanalysis.pdf (2.3 MB)

Topics:

• Detector Characterization
• Education, Outreach

Authors:

• Gerhard Heinzel
• Albrecht Ruediger
• Roland Schilling

Keywords:

Fourier Transform Spectral Density Decibels

Referenced by:

• LIGO-T1800210-v2: Signal Processing for the Practical Physicist: Control Loop (Controls) Design Class