Optimized Local Trigonometric Bases
Gregory Matviyenko · Applied and Computational Harmonic Analysis · 1996
This paper generalizes Malvar–Coifman–Meyer (MCM) wavelets by extending the choice of bell functions. We dispense with the orthonormality of MCM wavelets to produce a family of smooth local trigonometric bases that efficiently compress trigonometric functions. Any such basis is, in general, not orthogonal, but any element of the dual basis differs from the corresponding element of the original basis only by the shape of the bell. Furthermore, in our scheme the bell functions are bounded by 1 and the dual bell functions are bounded by (21/2+ 1)/2 ≈1.2. These bounds ensure the numerical stability of the forward and the inverse transformations in these bases. Numerical examples demonstrate that in many cases the proposed bases provide substantially better (up to a factor of two) compression than the standard MCM wavelets.