Fast Continuous Wavelet Transform Based on B-Splines

摘要

The Continuous Wavelet Transform (CWT) is an effective way to analyze nonstationary signals and to localize and characterize singularities. Fast algorithms have already been developed to compute the CWT at integer time points and dyadic or integer scales. We propose here a new method that is based on a B-spline expansion of both the signal and the analysis wavelet and that allows the CWT computation at arbitrary scales. Its complexity is O(N), where N represents the size of the input signal; in other words, the cost is independent of the scale factor. Moreover, the algorithm lends itself well to a parallel implementation.