Computational Algorithms for Daubechies Least-Asymmetric, Symmetric, and Most-Symmetric Wavelets

Computational algorithms have been developed for generating min-length max-flat FIR filter coefficients for orthogonal and biorthogonal wavelets with varying degrees of asymmetry or symmetry. These algorithms are based on spectral factorization of the Daubechies polynomial with a combinatorial search of root sets selected by a desired optimization criterion. Daubechies filter families were systematized to include Real Orthogonal Least Asymmetric (DROLA), Real Biorthogonal symmetric balanced Most Regular (DRBMR), Complex Orthogonal Least Asymmetric (DCOLA), and Complex Orthogonal Most Symmetric (DCOMS). Total phase nonlinearity was the criterion minimized to select the roots for the DROLA, DCOLA, and DCOMS filters. Timedomain regularity was used to select the roots for the DRBMR filters (which have linear phase only). New filters with distinguishing features are demonstrated with examples.