New Approaches to Reduction of Computational Complexity in Signal Processing Systems
Mathematically, most computer-implemented signal processing activity can be represented as discrete form matrix-vector multiply or matrix inversion processes, wherein the matrix structure exhibits some form of symmetry with regard to a repetitious arrangement of elements in it. A direct computation approach to the implementation of these discrete mathematical processes, which ignores the nature of the symmetries, would require respectively O(n2) and O(n3) multiply operations for an n-order system. On the other hand, if one exploits the form of the matrix symmetry in the problem, it becomes possible to define partitioned solution approaches that significantly reduce the level of computation for these processes. Two well-known examples of such an exploitation are the use of the fast Fourier transform (FFT) method in implementing the generation of a discrete Fourier spectrum with O(n log2 n) multiply operations and the use of the Levinson recursive method in the solution of the Toeplitz equation problem with O(n2) multiply operations.
KeywordsFast Fourier Transform Computation Load Chinese Remainder Theorem Fermat Number Convolution Process
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