| Multirate filter banks are commonly used for data compression and communications. Recently, a special signal-adapted filter bank known as the principal component filter bank (PCFB) was shown to be simultaneously optimal for several objectives. However, PCFBs, which are defined over paraunitary (PU) filter bank classes, are only known to exist in the extremal cases where the analysis/synthesis polyphase matrix has zero and infinite memory. For many inputs, the infinite-order PCFB filters have unrealizable ideal bandpass response. When the polyphase matrix has finite memory or finite impulse response (FIR), PCFBs are not believed to exist, although this has not been proven.;The main contribution is to bridge the gap between the zero memory PCFB and the infinite-order one. To that end; several methods for designing realizable signal-adapted filter banks are presented. We show that a popular FIR PU filter bank design method, which only requires an FIR compaction filter; incurs exponential complexity due to the compaction filter nonuniqueness. To avoid this dilemma, we propose a method by which all filters are obtained together. The method involves finding an FIR PU least-squares approximant to the infinite-order PCFB. Exploiting a complete parameterization of FIR PU systems using canonical building blocks, an iterative greedy algorithm for solving the least-squares problem is presented. Simulations show that as the memory of the filter bank increases, the filter bank behaves more like the infinite-order PCFB in terms of several objectives.;In addition, we focus on designing signal-adapted filter banks in which the filters are FIR but otherwise unconstrained. By alternately optimizing the analysis and synthesis filters for mean-squared error, a different iterative greedy algorithm is proposed for designing such filter banks. Simulations show that the filter banks designed come close to the information theoretic rate-distortion bound.;Finally, we show how the eigenfilter technique used in the above algorithms can be used to design channel shortening equalizers, which arise in discrete multitone (DMT) systems. Unlike other methods requiring a Cholesky decomposition for every delay parameter, this technique only requires one for all values. Despite this complexity decrease, simulations show that the equalizers designed yield nearly optimal bit rate. |
