The auditory critical bands interpreted as a local Kautz transformation

Abstract

The Zwicker data describes the relation between the critical bands and the center frequencies of the auditory system. The data can roughly be divided into two parts. At the low center frequencies the critical bandwidth is constant. At the high center frequencies the bandwidth increases in a monotonie way with the center frequency. The following interpretation of this data is proposed. It is assumed that the auditory system performs a running orthogonal transformation, i.e., first the signal is windowed (localized in time) and next an orthogonal transformation is performed on the windowed signal. The constant bandwidth at the low center frequencies is interpreted as stemming from the (constant) window. The varying bandwidth at the high center frequencies can be modelled by a Kautz transformation. It is shown that such an interpretation holds not only qualitatively, but quantitatively as well.