Preprint Concept Paper Version 1 Preserved in Portico This version is not peer-reviewed

A Generic Scalable DFT Calculation Method for Vectors and Matrices Using Matrix Multiplications

Version 1 : Received: 8 March 2022 / Approved: 9 March 2022 / Online: 9 March 2022 (09:48:06 CET)
Version 2 : Received: 11 March 2022 / Approved: 11 March 2022 / Online: 11 March 2022 (11:03:46 CET)

How to cite: Khan, A.A. A Generic Scalable DFT Calculation Method for Vectors and Matrices Using Matrix Multiplications. Preprints 2022, 2022030129 (doi: 10.20944/preprints202203.0129.v1). Khan, A.A. A Generic Scalable DFT Calculation Method for Vectors and Matrices Using Matrix Multiplications. Preprints 2022, 2022030129 (doi: 10.20944/preprints202203.0129.v1).

Abstract

Computation of Discrete Fourier Transform (DFT) is a challenging task. Especially, on computational machines/embedded systems where resources are limited. The importance of Fourier Transform (FT) cannot be denied in the field of signal processing. In this paper, we propose a technique that can compute Discrete Fourier Transforms for a matrice or vector with the help of matrix multiplication. Moreover, we discuss the trivial methods used for computation of DFT along with methods based on matrix multiplication used to compute discrete Fourier Transform. Furthermore, we explain the shortcomings. Our method can help in the calculation of a Discrete Fourier Transformation matrix by truncation of values from our proposed generic method which can help in computing DFT of varying lengths of vectors. On computing machines and programming environments, having support for matrix multiplication, our proposed methodology can be implemented.

Keywords

Discrete Fourier Transform; Fourier Transform; Twiddle factor

Subject

MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics

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