Abstract
The wavelet transform is a time-frequency representation obtained by decomposing the signal onto localized functions that are translated and dilated. It defines an invertible and stable representation. Wavelet decompositions are found in the cochlea of the auditory system. Translational invariants are constructed by eliminating the phase of an analytic wavelet transform, with a modulus, and then calculating a spatial average. This defines a contracting operator. The logarithm of these invariants is similar to the MFCC descriptors used for audio signal classification. Unlike the Fourier transform, or windowed Fourier transform, these multi-scale descriptors are distortion-stable, even at high frequencies.
