Periodicity transforms
- 1 November 1999
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 47 (11), 2953-2964
- https://doi.org/10.1109/78.796431
Abstract
This paper presents a method of detecting periodicities in data that exploits a series of projections onto "periodic subspaces". The algorithm finds its own set of nonorthogonal basis elements (based on the data), rather than assuming a fixed predetermined basis as in the Fourier, Gabor, and wavelet transforms. A major strength of the approach is that it is linear-in-period rather than linear-in-frequency or linear-in-scale. The algorithm is derived and analyzed, and its output is compared to that of the Fourier transform in a number of examples. One application is the finding and grouping of rhythms in a musical score, another is the separation of periodic waveforms with overlapping spectra, and a third is the finding of patterns in astronomical data. Examples demonstrate both the strengths and weaknesses of the method.Keywords
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