Proportional bandwidth spectrum analysis in a synthetic instrument

Spectrum analyzers used in communication systems are traditionally modeled by a bank of filters with equally spaced frequency centers and bandwidths. This type of spectrum analyzer decomposes the input signal into basis functions that share common features such as time extent and bandwidth. Another important class of spectrum analyzers is the proportional bandwidth spectrum analyzer modeled by a bank of filters where the spacing between spectral centers and bandwidths increase as a function of the frequency of interest. The filter spacing and bandwidth are seen to have equally spaced centers and equal bandwidths on a logarithmic scale. This type of spectrum analyzer decomposes the input signal into basis functions that share a scaled range of features such as varied time duration and varied bandwidths. Analysis of mechanical systems such as vibrating beams, acoustic resonators, cochlear of the human ear, whale and dolphin sounds, harmonic-rich FM waveforms, and image features are best performed by proportional bandwidth analyzers. This paper presents and analyzes the performance of an extremely efficient implementation of a proportional bandwidth filter bank.