Abstract
Abstract A new type of perfect reconstruction filter bank is presented in this paper. This new class of filter bank has the following distict features at the same time: linear-phase, distortion-free, hR-FIR filter pair, closed-formexpression, orthogonal projection, and factorization-free. In contrast, the other existing filter banks do not possessall these properties simutaneously. For example, the classic Quadrature Mirror Filter (QMF) does not have theperfect reconstruction nature. Another example is the Conjugate Quadrature Filter (CQF), which lacks the linear-phase property. A qualitative comparison of different types of filter banks is also included. This newly developed perfect reconstruction hR-FIR filter bank is then extended to the 2-D case. Both separable and non-separable filters are considered. In addition, both rectangular dowusampling and non-rectangular downsampling schemesare discussed. Numerical optimization procedures are used to compute the optimal filter coefficients. The resultsare listed in tables for quick reference.
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