A GENERALIZED WAVELET TRANSFORM FOR FOURIER-ANALYSIS - THE MULTIRESOLUTION FOURIER-TRANSFORM AND ITS APPLICATION TO IMAGE AND AUDIO SIGNAL ANALYSIS

A wavelet transform specifically designed for Fourier analysis at multiple scales is described and shown to be capable of providing a local representation which is particularly well suited to segmentation problems. It is shown that, by an appropriate choice of analysis window and sampling intervals, it is possible to obtain a Fourier representation which can be computed efficiently and overcomes the limitations of using a fixed scale of window, yet by virtue of its symmetry properties allows simple estimation of such fundamental signal parameters as instantaneous frequency and onset time/position. The transform is applied to the segmentation of both image and audio signals, demonstrating its power to deal with signal events which are localized in either time/space or frequency. Feature extraction and segmentation are tackled through the introduction of a class of multiresolution Markov models, whose parameters represent the signal events underlying the segmentation. In the case of images, this provides a unified and computationally efficient approach to boundary curve segmentation. In audio analysis, it provides an effective way of note segmentation, giving accurate estimates of onset time and pitch in polyphonic musical signals