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A generalized wavelet transform for Fourier analysis: the multiresolution Fourier transform and its application to image and audio signal analysis

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3 Author(s)
Wilson, R. ; Dept. of Comput. Sci., Warwick Univ., Coventry, UK ; Calway, A.D. ; Pearson, E.R.S.

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 performed through the introduction of a class of multiresolution Markov models, whose parameters represent the signal events underlying the segmentation.<>

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Information Theory, IEEE Transactions on  (Volume:38 ,  Issue: 2 )