Intraframe time-scaling of nonstationary sinusoids within the phase vocoder

An observation regarding the nature of the spectrum of a windowed swept-frequency sinusoid is exploited to time-scale (stretch or compress) time-variant sinusoids within the window or frame of an otherwise basic phase vocoder process. Nonstationary sinusoids are more closely represented as a series of windowed linearly swept sinusoids than as a series of windowed constant frequency sinusoids. Both the frequency sweep rate and the amplitude ramp rate can be identified and modified according to the time-scale ratio. The mathematics outlining this concept will be developed in the continuous time domain whereas a MATLAB program demonstrating the concept is in discrete time. An example is shown, using a swept and ramped sinusoid, that there are visible differences between using this correction and not using it. These differences predictably get more pronounced as the time rate of change of frequency or amplitude increases.