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Fast FIR Algorithms for the Continuous Wavelet Transform From Constrained Least Squares

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1 Author(s)
Leigh, G.M. ; Dept. of Agric., Fisheries & Forestry, St. Lucia, QLD, Australia

New algorithms for the continuous wavelet transform are developed that are easy to apply, each consisting of a single-pass finite impulse response (FIR) filter, and several times faster than the fastest existing algorithms. The single-pass filter, named WT-FIR-1, is made possible by applying constraint equations to least-squares estimation of filter coefficients, which removes the need for separate low-pass and high-pass filters. Non-dyadic two-scale relations are developed and it is shown that filters based on them can work more efficiently than dyadic ones. Example applications to the Mexican hat wavelet are presented.

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Signal Processing, IEEE Transactions on  (Volume:61 ,  Issue: 1 )