Analysis filterbank with arbitrary frequency and bandwidth using a multitaper technique

Abstract

Acoustical signals are often analyzed for power spectral density. The computational efficiency of the fast Fourier transform (FFT) for the short-time Fourier transform (STFT) is attractive in many contexts, but some applications require nonuniformly spaced analysis frequencies with different bandwidths. Two common examples are the mel frequency scale for speech signals and the constant Q or logarithmic frequency scale analysis of musical signals. These analyses are usually implemented with polyphase filterbanks, wavelets, or an ad hoc technique. This research presents a new method that allows arbitrary analysis frequencies and variable bandwidths. The method is based on the multitaper approach from nonparametric spectral estimation. Consequently, this method preserves the benefits of the multitaper approach, namely improved bias and variance properties when compared with the regular STFT-based approach. The multitaper method requires O(NM) computations, where N is the data segment length and M is the number of analysis frequency channels. This is the same order of growth exhibited by the straight discrete Fourier transform with the same N and M. [Work supported by NSF Ocean Sciences.]