Multi-Taper spectra: a Mathematica 8-TM function

Abstract

Two simple functions written in Mathematica 8 TM are here presented for a rapid multitaper spectral estimation. Multitaper ensures an optimal spectral smoothing, as it reduces the variance of the amplitude spectrum estimates using the technique of tapering the time series with a set of orthogonal functions, and then optimally averaging the FFT of the tapered signals. The first Function uses the Slepian n_ prolate functions as tapers, while the second Function uses Hermite Functions as tapers. Both Routines are tested using a synthetic time serie as input. Multitaper smoothing is often used in the spectral analysis of seismic and other geophysical data. The present functions may be useful for geophysicists who are Mathematica 8 TM users.