Abstract

An important problem in speech technology is the modification of the time scale of an audio signal by stretching or contracting without degrading the signal intelligibility. Simple time scaling by recording at a different speed (or by interpolation/decimation of samples) obviously modifies the signal spectrum and therefore degrades intelligibility. We report a new approach based on determining the Wigner distribution function (WDF), scaling its time dependence without changing its frequency dependence, and finding the signal whose WDF is as close as possible to the modified function. Let S(t) be a signal whose time is to be modified by the transformation t’ = h(t). We determine its WDF W(t,ω) and modify it to obtain a new 2-D function W₀(t,ω) = W[h(t),ω]. The function W₀(t,ω) is not necessarily an admissible WDF. We find a modified signal S'(t) whose WDF W’(t,ω) best approximates W₀(t,ω). This is accomplished by projecting W₀(t,ω) on the class of 2-D functions that are admissible WDFs. The result involves solving an eigenvalue problem whose eigenfunction of largest eigenvalue is the desired signal. Possible implementations are presented. A suboptimal signal S'(t) may be obtained by applying an optimal linear transformation on W₀(t,ω). The operation can be implemented using an optical processor.

© 1986 Optical Society of America