Download Redressing Warped Wavelets and Other Similar Warped Time-something Representations
Time and frequency warping provide effective methods for fitting signal representations to desired physical or psychoacoustic characteristics. However, warping in one of the variables, e.g. frequency, disrupts the organization of the representation with respect to the conjugate variable, e.g. time. In recent papers we have considered methods to eliminate or mitigate the dispersion introduced by warping in time frequency representations and Gabor frames. To this purpose, we introduced redressing methods consisting in further warping with respect to the transformed variables. These methods proved not only useful for the visualization of the transform but also to simplify the computation of the transform in terms of shifted precomputed warped elements, without the need for warping in the computation of the transform. In other linear representations, such as time-scale, warping generally modifies the transform operators, making visualization less informative and computation more difficult. Sound signal representations almost invariably need time as one of the coordinates in view of the fact that we normally wish to follow the time evolution of features and characteristics. In this paper we devise methods for the redressing of dispersion introduced by warping in wavelet transforms and in other expansions where time-shift plays a role.