A linear periodically time-varying filter for time-frequency scaling of speech

A method is introduced for finding a signal fˆ(n ) with a time-varying spectrum Cˆ(nω) approximating a geometric transformation C(αn,βω) in the mean-square sense. The phases of C(n,ω) and C(αn ,βω) are allowed to differ by a smooth function of n and ω selected to minimize the overall difference between these complex functions. The result is a periodically time-varying filter relating fˆ(n) and f(n), which is easy to implement, requiring few arithmetic operations per output sample. The method shows high fidelity in recovering the original signal from its scaled version. It is shown that for the same bit rate reduction, joint time-frequency scaling renders higher signal-to-noise ratios than either time-only or frequency-only scaling