A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals.

Pablo Soto-Quiros

doi:10.1155/2015/348517

Abstract

This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

Highlights

Let l2(Zn, Cd) be the space of vector-valued discrete-time signals with n samples, where each sample is a complex vector of length d
This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT
The vector-valued DFT is used in digital signal processing, for example, the study of new complex valued constant amplitude zero autocorrelation (CAZAC) signals [9], which serve as coefficients for phase coded waveforms with prescribed vector-valued ambiguity function behavior, which is relevant in light of timefrequency analysis, vector sensor, and MIMO technologies [7]

Summary

Introduction

Let l2(Zn, Cd) be the space of vector-valued discrete-time signals with n samples, where each sample is a complex vector of length d. (2) Reducing the elapsed time to compute the vectorvalued DFT of a vector-valued discrete-time signal using parallel computing through aforementioned new mathematical framework This new framework is developed with a set of block matrix operations, for example, Kronecker product, direct sum, stride permutation, vec operator, and vec inverse operator (see Section 2.1 for details). This mathematical framework contributes to implementation of parallel algorithms.

Background

DFT for Vector-Valued Signals

Implementation and Experimental Investigation

Conclusion