### ASA 125th Meeting Ottawa 1993 May

## 2aNS6. Wavelet analysis of rhythm.

**Neil P. McAngus Todd
**

**
**
*Dept. of Music, City Univ., Northampton Square, London EC1V 0HB, England
*

*
*
The application of wavelet analysis to rhythm is described. Rather than
carry out the multiscale decomposition on the sound signal itself this method
decomposes the sound energy flux [N. P. McAngus Todd, J. Acoust. Soc. Am. 92
(A), 2380 (1992)], This enables the analysis of rhythmic phenomena that have
frequencies several orders of magnitude below pitch and are not represented in
the sound signal. The decomposition is carried out by a logarithmically spaced
Laguerre series approximation Gaussian filter bank. The analog design was
discretized to a cascaded IIR structure using a bilinear transformation. This
has the following advantages over the usual FIR approach: (a) plausibility of
interpretation as a perceptual model since the ideal Gaussian is not physically
realizable; (b) a smaller number of parameters; (c) smaller delay times than
the Gaussian ideal; (d) avoidance of the need for down/up sampling. Two
complementary structural components are obtained from the projection in the
frequency-time plane of loci of zero crossings in the rate of change of energy:
(a) segmentation structure, corresponding to positive second derivatives; (b) a
stress structure, corresponding to negative second derivatives. A compact tree
coding of rhythm is possible from points of convergence of the loci of zero
crossings.