Warped Frames: Dispersive vs. Non–dispersive Sampling

Conventional Time-Frequency and Time-Scale Representations are often too rigid to capture fine details of sound or musical signals. Adaptation of ideal time-frequency tilings is often desirable in order to represent the signal in terms of components that are meaningful from a physical or perceptual point of view. Remapping of the time and frequency axes by means of time and frequency warping can help achieve the desired flexibility of the representation. However, in the general case, the conjugate variable is affected as well, so that the resulting representation plane is distorted. In this paper we show methods to redress the conjugate distortion introduced by warping, both in the unsampled case of the integral Short-Time Fourier Transform and in the sampled case of generalized Gabor frames. AMS Primary 42C15: Time-Frequency Representations, Short-Time Fourier Transform, Gabor Frames, Frequency Warping, Time Warping, Signal Analysis