Comb and multiplexed wavelet transforms and their applications to signal processing

As an extension of wavelet theory, new wavelet bases that are discrete in nature and suitable for the analysis and synthesis of pseudo-periodic digital signals are introduced. By means of these bases, the signal is represented in terms of a periodic trend and aperiodic fluctuations at several scales. In the frequency domain, the periodic trend lies in bands that are centered on the harmonics while the fluctuations are distributed in several sidebands. Properties of comb and multiplexed wavelet transforms are examined and the concepts applied to the analysis of real-life signals. In one dimension, the new transforms have interesting applications to speech and music signal processing. Their extension to two dimensions may be useful for the analysis of pseudo-periodic images