Broadband Spectral Estimation Using the Multiple Window Method: A Comparison with Classical Techniques

摘要

The Multiple Window recently introduced by D.J. Thomson is an alternative approach to spectral estimation. Using an orthogonal decomposition of the Discrete Fourier Transform of the data on the prolate spheroidal wave sequences, the power spectrum is estimated by a weighted average of raw spectra obtained from the Fourier transforms of the data windowed by the prolate sequences. This method has the reputation of working well on short data sequences, offering good variance control and a fair resolution. Because the Multiple Window technique combines Fourier transforms with data adaptive weighting, it is compared, in a Monte Carlo simulation, to more conventional spectral estimation methods: the classic averaged Fourier transforms technique and Capon's Maximum Likelihood method. The underlying spectral density to be estimated is of an ARMA process simulating underwater acoustic ambient noise. It is characterized by a moderate dynamic range of 30 dB and can be regarded as a generic spectrum of many applications. The three methods considered here are non parametric, so that no estimator has an unfair advantage. The normalized bias, random and root mean square errors, as well as the statistical distributions, based on 512 realizations of the spectral density, quantify the performance of the three different techniques. (MJM)