Information Processing Using Circulant Matrices

Abstract

Circulant matrices may be used to process certain kinds of signals in computer science applications. Specifically, they can be used as signal transforms. In this thesis several new applications of circulant matrices are described. New results have been obtained in number theoretic Hilbert transform (NHT), which is a generalization of discrete Hilbert transform (DHT).The NHT matrix generates ideal orthogonal sequences named as random residue sequences, since the NHT matrix with its transpose computes all correlation in the block. Random residue sequences can be used as carriers for wireless communications. We also investigate applications of circulant matrices to store and reproduce patterns as neural memories.