The Fourier-Mellin transform and mammalian hearing.

A combined Fourier–Mellin transform yields a representation of a signal that is independent of delay and scale change. Such a representation should be useful for speech analysis, where delay and scale differences degrade the performance of correlation operations or other similarity measures. At least two different versions of a combined Fourier–Mellin transform can be implemented. The simplest version (the ‖F‖2−‖M‖2 transform) completely eliminates spectral phase information, while a slightly more complicated version (the ?−? transform) preserves some phase information. Both versions can be synthesized with a Fourier transform and an exponential‐sampling algorithm. Exponential sampling produces a frequency scale distortion that is similar to the effect of the cochlea. The ‖F‖2−‖M‖2 transform can also be implemented with a bank of proportional bandwidth filters. If the relative phase between spectral components is preserved, then a Fourier–Mellin transformer can perform compression of linear‐period modulat...