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

• Published in: IEEE transactions on information theory Vol. 38; no. 2; pp. 674 - 690
• Main Authors: Wilson, R., Calway, A.D., Pearson, E.R.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.1992; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Exact sciences and technology; Fourier transforms; Image analysis; Image processing; Image resolution; Image segmentation; Information, signal and communications theory; Signal analysis; Signal processing; Signal resolution; Telecommunications and information theory; Vectors; Wavelet analysis; Wavelet transforms; Image analysis; Parameter estimation; Fourier transformation; Segmentation; Acoustic signal; Wavelet transformation; Video signal; Harmonic analysis; Markov model; Signal analysis; Image reconstruction
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.119730

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.< >