Periodicity transforms

Author

Sethares, William A. ; Staley, Thomas W.

Author_Institution

Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI, USA

Volume

47

Issue

11

fYear

1999

fDate

11/1/1999 12:00:00 AM

Firstpage

2953

Lastpage

2964

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

acoustic signal processing; astronomical techniques; music; pattern recognition; signal processing; spectral analysis; transforms; astronomical data; linear-in-period approach; musical score; nonorthogonal basis elements; overlapping spectra; periodic subspaces; periodic waveforms; periodicity transforms; projections; rhythms; Algorithm design and analysis; Auditory system; Covariance matrix; Fourier transforms; Frequency; Karhunen-Loeve transforms; Rhythm; Speech; Visual system; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.796431

Filename

796431