Fast algorithms to design discrete Wiener filters in lag and length coordinates
Milton José Porsani · Geophysics · 1996
Abstract Two recursive algorithms for designing discrete Wiener filters for wavelets of different phase characteristics are the Simpson and the Manolakis recursions. Both procedures are efficient; however, both recursions work with a prefixed length filter. Two fast algorithms to design discrete Wiener filters in lag and length coordinates are presented. The recursion methods of Levinson and Manolakis are combined to generate two fast algorithms that calculate the value for the minimized total squared error (MTSE) corresponding to spiking and shaping filters. For a spiking filter of length n and a wavelet of m data points, 5mn + 5/2n2 + 3/2n operations are required to obtain the (m + n −1) × n map of the MTSEs, (one operation is defined here as one multiplication and one addition). For a shaping filter, 4mn + 3/2(n2 + n) operations are required to obtain the corresponding m × n map. These algorithms may be seen as a Levinson recursion on two variables, length j of the filter and lag k, for the desired signal. Numerical examples for spiking and shaping filters are presented.