22 March 1996 Harmonic wavelets, constant Q transforms, and the cone kernel TFD
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Proceedings Volume 2762, Wavelet Applications III; (1996); doi: 10.1117/12.236016
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States
Abstract
In this research we compare general harmonic wavelet transforms (GHWT), constant Q transforms (CQT) and the Cone kernel time-frequency distribution (CKTFD) for the analysis of musical signals. The first two consist of a series of band pass filters that have a constant Q (quality), each of which correspond to a semitone interval (or better) in the musical scale. The CKTFD is not a constant Q type transform but belongs to the more general class of bilinear time-frequency distributions with the special property of reducing the (usually) undesirable interference terms common in these types of distributions. Their computation schemes are compared and the advantages of each discussed. All three have a structure that may be easily parallelized. We used the three methods to analyze a musical note (middle C) played on an electric piano. There are subtle differences in the results of the methods. All three quite clearly show the first four harmonics of the musical note (C4). However, the CQT reveals that harmonics higher than four extend in time for almost the entire duration of the note. Neither the GHWT nor the CKTFD show harmonics higher than four for the entire length of the signal, though they do reveal them (i.e., frequencies higher than 1024 Hz.) at the initiation of the note. The power spectrum of the signal does reveal harmonics from one through four as having most of the power but harmonics five through ten are also revealed. Unfortunately, the time variation of the signal cannot be extracted from the power spectrum hence the use of time-frequency or time-scale diagrams. Aside from musical applications, such methods would be useful for t-f analysis of vibrating machinery.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Samir R. Chettri, Yuko Ishiwaka, H. Kimura, Isamu Nagano, "Harmonic wavelets, constant Q transforms, and the cone kernel TFD", Proc. SPIE 2762, Wavelet Applications III, (22 March 1996); doi: 10.1117/12.236016; https://doi.org/10.1117/12.236016
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KEYWORDS
Wavelets

Transform theory

Fourier transforms

Medium wave

Signal analyzers

Wavelet transforms

Heat treatments

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