An Implementation of the “algorithme à trous” to Compute the Wavelet Transform

The computation of the wavelet transform involves the computation of the convolution product of the signal to be analysed by the analysing wavelet. It will be shown that the computation load grows with the scale factor of the analysis. We are interested in musical sounds lasting a few seconds. Using a straightforward algorithm leads to a prohibitive computation time, so we need a more effective computation procedure.