Wavelet analysis of rhythm
Neil P. McAngus Todd · The Journal of the Acoustical Society of America · 1993
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) segmentationstructure, corresponding to positive second derivatives; (b) a stressstructure, corresponding to negative second derivatives. A compact tree coding of rhythm is possible from points of convergence of the loci of zero crossings.