Fast CWT computation at integer scales by the generalized MRAstructure

This article proposes a fast algorithm for continuous wavelet transform (CWT) at linear scale without decimation by using the generalized multiresolution analysis (MRA) structure. The constraints required on the lowpass and bandpass filters in the generalized MRA structure are derived. A possible solution for the lowpass filters and a least-squares design of the bandpass filters are given. The computational complexity of the algorithm is O(N) per scale, where N is the data length. The fast algorithm is verified by computer simulations