Critical band analysis-synthesis

The formal derivation of a transformation which models the frequency selective properties (critical bandwidths) of the auditory system is developed. A parameterized family of constant-Q analysis-synthesis transform pairs is developed from a property of homogeneous functions. This formulation allows for a wide choice of selections for center frequencies, bandwidths, and filter shapes. A particular member of the transform family is implemented to model the frequency selective properties of the peripheral auditory system. With this transform, short-time spectral analysis using critical band filter shapes can be implemented. In the absence of spectral modification, the analysis-synthesis transform can be made arbitrarily close to an identity system. This new approach to analysis-synthesis provides the necessary mathematical support needed to design and optimize both constant-Q and critical band analysis-synthesis transforms.