High-resolution spectral analysis with arbitrary spectral centers and arbitrary spectral resolutions

Spectral decomposition via banks of narrowband filters is a classic method of analyzing broadband acoustic signals. FFT algorithms and hardware efficiently perform narrowband analysis but are limited to constant bandwidths at fixed spectral center frequencies. We develop a technique for processing FFT outputs to realize banks of narrowband filters for which spectral band centers and spectral bandwidths may be arbitrarily assigned. In particular we present spectral analyzer configurations with spectral centers uniformily spaced on a logarithmic scale and with bandwidths proportional to center frequencies (constant Q filters) or with bandwidths proportional to the square root of center frequencies (root-proportional filters for linear FM line tracking).