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Fast Continuous Wavelet Transform

M.J. Vrhel, C. Lee, M. Unser

Proceedings of the Twentieth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'95), Detroit MI, USA, May 8-12, 1995, vol. II, pp. 1165-1168.



We introduce a general framework for the efficient computation of the continuous wavelet transform (CWT). The method allows arbitrary sampling along the scale axis, and achieves O(N) complexity per scale where N is the length of the signal. Our approach makes use of a compactly supported scaling function to approximate the analyzing wavelet. We derive error bounds on the wavelet approximation and show how to obtain any desired level of accuracy through the use of higher order representations. Finally, we present examples of implementation for different wavelets using polynomial spline approximations.


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