A fast algorithm of Continuous Wavelet Transform based on Mellin Transform with biomedical application

A fast implementation of the Continuous Wavelet Transform (CWT) which is based on the Merlin Transform is presented. The algorithm has two major characteristics, one is that it calculates the wavelet coefficients of different scales simultaneously at a given time instant; the other is that it can analyze the signal at scales very finely sampled with a common ratio. For each time point, computer implementation can be realized with three FFTs (one forward FFT and two inverse FFTs) all of length 2N (N is the number of scales). It is a fast CWT algorithm suitable for use when the signal is to be analyzed at scales finely distributed over a relatively narrow span.