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.