Soma por Partes para Sinais Periódicos e Transformadas Discretas

Abstract

Resumo-O algoritmo de soma por partesé analisado eé proposta uma modificação para o caso de sinais periódicos. Uma expressão geral para a soma por partes iteradaé obtida. A técnica proposta pode ser empregada para reescrever transformadas discretas em um formalismo alternativo, permitindo o desenvolvimento de novos algoritmos rápidos. Palavras-Chave-Soma por partes, sinais periódicos, transformadas discretas.

Efficient Computation of the 8-point DCT via Summation by Parts

“…Above expression can be simplified with the assumption of the following additional weak conditions. Admitting that the considered signals are periodic with period N , it was established in [30] that:…”

“…The aim of this paper is to propose a new fast algorithm for the 8-point DCT computation based on the summationby-parts formula for periodic signals [23,30]. The introduced method is sought to achieve the theoretical minimal multiplicative complexity for the exact DCT computation [31,32].…”

“…Although applied in several contexts such as computational physics for approximate second derivatives [25], approximations of the linear advection-diffusion equation in computational fluid dynamics [26], and rapid calculation of slow converging series in electromagnetic problems [27], it has been particularly overlooked by the signal processing community. Early attempts to employ it as a numerical analysis tool are due to Boudreaux-Bartels and collaborators in the context of the DFT computation [28] and the evaluation of Fourier coefficients errors calculations [29].The aim of this paper is to propose a new fast algorithm for the 8-point DCT computation based on the summationby-parts formula for periodic signals [23,30]. The introduced method is sought to achieve the theoretical minimal multiplicative complexity for the exact DCT computation [31,32].…”