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

## TL;DR

This paper introduces a new parallel framework for efficiently computing the Fourier transform of vector-valued signals using block matrices.

## Contribution

The novel contribution is a parallel implementation of the vector-valued DFT using block matrix operations for multicore processors.

## Key findings

- Using multicore processors reduces execution time for vector-valued DFT computations.
- Speedup increases with more logical processors and longer signal lengths.

## 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.