Modern techniques of power spectrum estimation

Abstract

The paper discusses the impact of the fast Fourier transform on the spectrum of time series analysis. It is shown that the computationally fastest way to calculate mean lagged products is to begin by calculating all Fourier coefficients with a fast Fourier transform and then to fast-Fourier-retransform a sequence made up of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a_{k}^{2}+b_{k}^{2}</tex> (where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a_{k}+ib_{k}</tex> are the complex Fourier coefficients). Also discussed are raw and modified Fourier periodograms, bandwidth versus stability aspects, and aims and computational approaches to complex demodulation. Appendixes include a glossary, a review of complex demodulation without fast Fourier transform, and a short explanation of the fast Fourier transform.