Approach to the design of discrete-time wavelets
Huai D. Li, V.K. Jain · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
The paper presents an approach to the design of half-band discrete-time wavelets. This is accomplished through the use of a class of quadrature mirror filters which exhibit near- perfect reconstruction property. In particular, we present a technique for the design of such filters, wherein the designer has the flexibility to make tradeoffs between in- band behavior, out-of-band behavior, and the transition-band behavior. The basic formulation is carried out in the frequency domain, which is shown to translate the design problem into an eigenvalue-eigenvector problem. To find the optimal filter for a specific set of specifications, an optimization algorithm is also presented. Using this algorithm, designs ranging from 4 to 80 taps have been carried out successfully. A fairly complete table of resulting filters, which can be used by signal and image processing engineers, is included in the paper.