Filter design for CWT computation using the Shensa algorithm

Direct computation of the continuous wavelet transform (CWT) using FFT requires O (Nlog₂N) operations per scale, where N is the data length. The Shensa (1992) algorithm is a fast algorithm to compute the CWT that uses only O(N) operations per scale. The application of the algorithm requires the design of a bandpass and a lowpass filter for a given mother wavelet function. Previous design method involves multi-dimensional numerical search and is computationally intensive. This paper proposes an iterative method to design the optimum filters. It computes in each iteration least-squares solutions only and does not need numerical search. The proposed filter design method is corroborated by simulations