Matrizes Autossimilares: Definições e Cenários de Aplicação em Processamento de Sinais

This work introduces the concepts of self-similar matrix and quasi self-similar matrix, as well as a metric between a quasi self-similar matrix and a self-similar matrix of its class. A systematic method for converting a quasi self-similar matrix into a self-similar matrix and possible adjustment factors is presented. A method of expanding an arbitrary self-similar matrix as a linear combination of rank-one matrices is presented. As an illustration of the proposed techniques, optimum algorithms for computing a DFT of blocklength 8 and a cyclic convolution of blocklength 4 are obtained.