Fast forms of banded maps

A decomposition technique for linear algorithms called the concurrent triple product (CTP) structure is tested on a class of maps which are diagonally banded. The banded maps include Toeplitz, convolution, and Hilbert transform operations, each of which is considered. The CTP and its interrelationship with array architectures is discussed. The concept of computational reassignment is introduced. This technique takes advantage of matrix sparsity to simplify the CTR expansion. While considering the Hilbert transform, it is shown that computational reassignment in the limit becomes a complete reorganization of the algorithm. Thus, the CTP decomposition can be viewed as a family of techniques.<
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