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Sound Analysis and Synthesis through Complex Bandpass Filter Banks

In this paper a new algorithm to compute an additive synthesis model of a signal is presented. An analysis based on the Complex Continuous Wavelet Transform has been used to extract the time-varying amplitudes and phases of every component of the additive model. The mathematical relationships between the CCWT, the Hilbert Transform and complex filter banks are presented in order to obtain useful filter bank design parameters. The mathematical analysis of five different signals is presented: a pure cosine, a sum of cosines, a signal with frequency variations and two finite duration signals with Gaussian and exponential envelopes. The obtained theoretical results are finally compared with those computed with the developed algorithm.

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