RAPID COMPUTATION OF THE CONTINUOUS WAVELET TRANSFORM BY OBLIQUE PROJECTIONS

We introduce a fast simple method for computing the real continuous wa velet transform (CWT), The approach has the following attractive featu res: It achieves O(N) complexity per scale, the filter coefficients ca n be analytically obtained by a simple integration, and the algorithm is faster th;ln a least squares approach with negligible loss in accur acy, Our method is to use P wavelets per octave and to approximate the m with their oblique projection onto a space defined by a compactly su pported scaling function, The wavelet templates are expanded to larger sizes (octaves) using the two-scale relation and zero-padded filterin g, Error bounds are presented to justify the use of an oblique project ion over an orthogonal one. All the filters are FIR with the exception of one filter, which is implemented using a fast recursive algorithm.