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A Generalized Wavelet Transform for Fourier Analysis: the Multiresolution Fourier Transform and its Application to Image and Audio Signal Analysis

R. Wilson, A. D. Calway, E. R. S. Pearson, A Generalized Wavelet Transform for Fourier Analysis: the Multiresolution Fourier Transform and its Application to Image and Audio Signal Analysis. IEEE Transactions on Information Theory, 38 (2). ISSN 0018-9448, pp. 674–690. March 1992. No electronic version available.

Abstract

A wavelet transform specifically designed for Fourier analysis at multiple scales is described and shown capable of providing a \em 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 localised 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.

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