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Research Report CS-RR-204

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R.G. Wilson, A.D. Calway, E.R.S. Pearson and A.R. Davies, An Introduction to the Multiresolution Fourier Transform and its Applications (June 1, 1992).

Abstract

The Multiresolution Fourier Transform (MFT) is a new tool for signal analysis which is designed with the express intent of providing a local signal representation adapted to the problem of segmenting signals into s set of meaningful primitive features. It is shown that this requires a signal representation that is richer than conventional Short Time Fourier Transforms (STFT) or indeed Wavelet Transformations (WT), but shares with them the property of giving a phase-space description of the signal. These considerations lead to the new transform, which can be seen as a marriage of the STFT and WT which overcomes the limitations of either as a signal representation for segmentation. Some of the elementary properties of the MFT are then discussed and its implementation for discrete signals is considered. The report is concluded with a summary of results obtained with the MFT on audio and image signal segmentation.

Download

The report may be downloaded in eight parts: cs-rr-204.1.ps.gz, cs-rr-204.2.ps.gz, cs-rr-204.3.ps.gz, cs-rr-204.4.ps.gz, cs-rr-204.5.ps.gz, cs-rr-204.6.ps.gz, cs-rr-204.7.ps.gz, cs-rr-204.8.ps.gz

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