Signal Processing on Finite Groups

摘要

A unified approach to the design and evaluation of fast algorithms for discretesignal processing is developed. Based on the theory of finite groups, it hence includes the familiar cases of the fast Fourier and Walsh-Hadamard transforms. However, the use of noncommutative groups reveals a large variety of novel methods. Some of these exhibit a superior performance, as measured by both reduced error rates and computational complexity, on nonstationary data. The recent history of this subject is reviewed first, followed by a detailed examination of the three principal ingredients of the present study: the underlying groups, the signal-processing tasks on which the group-based algorithms are to compete, and the signal models used to define the data environment. Test results and conclusions then follow, the former being based on the use of random correlation matrices. (kr)