High-Selectivity Filter Banks for Spectral Analysis of Music Signals

Abstract

This paper approaches, under a unified framework, several algorithms for the spectral analysis of musical signals. Such algorithms include the fast Fourier transform (FFT), the fast filter bank (FFB), the constant-Q transform (CQT), and the bounded-Q transform (BQT), previously known from the associated literature. Two new methods are then introduced, namely, the constant-Q fast filter bank (CQFFB) and the bounded-Q fast filter bank (BQFFB), combining the positive characteristics of the previously mentioned algorithms. The provided analyses indicate that the proposed BQFFB achieves an excellent compromise between the reduced computational effort of the FFT, the high selectivity of each output channel of the FFB, and the efficient distribution of frequency channels associated to the CQT and BQT methods. Examples are included to illustrate the performances of these methods in the spectral analysis of music signals.