Estimation of the instantaneous amplitude and the instantaneous frequency of audio signals using complex wavelets

This work presents a method of analyzing and synthesizing audio signals that uses complex wavelets. In the method, the input signal is filtered by a complex bandpass filter bank through a discrete version of the complex continuous wavelet transform. A general theoretical signal with time-dependent amplitude and phase has been analyzed. The analysis of the information provided by the modulus and the phase of the complex continuous wavelet transform was used to develop an additive analysis/synthesis algorithm for audio signals called complex wavelet additive synthesis. To illustrate the method, this new algorithm has been used to analyze the following four synthetic, non-stationary signals that have different frequency variation laws: a linear chirp, a quadratic chirp, a hyperbolic chirp and an FM signal with a sinusoidal excursion. Finally, the validity of the algorithm has been tested by comparing the results of an analysis of two real sounds with the proposed algorithm and with one existing technique, namely spectral modelling synthesis (SMS).