A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Classification of EEG signals using the wavelet transform
Signal Processing
Continuous wavelet transform with arbitrary scales and O(N) complexity
Signal Processing
Signal Processing - Special section: Hans Wilhelm Schüßler celebrates his 75th birthday
Multiridge detection and time-frequency reconstruction
IEEE Transactions on Signal Processing
Characterization of signals by the ridges of their wavelettransforms
IEEE Transactions on Signal Processing
Signal energy distribution in time and frequency
IEEE Transactions on Information Theory
Fast algorithms for discrete and continuous wavelet transforms
IEEE Transactions on Information Theory - Part 2
Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies
IEEE Transactions on Information Theory - Part 2
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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).