Preprint Concept Paper Version 2 Preserved in Portico This version is not peer-reviewed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.v2). Khan, A.A. A Generic Scalable DFT Calculation Method for Vectors and Matrices Using Matrix Multiplications. Preprints 2022, 2022030129 (doi: 10.20944/preprints202203.0129.v2).

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. This paper proposes a technique that can compute Discrete Fourier Transforms for a matrice or vector with the help of matrix multiplication. Moreover, this paper discusses the trivial methods used for computation of DFT along with methods based on matrix multiplication used to compute discrete Fourier Transform in addition to the shortcomings. The proposed method can help in the calculation of a Discrete Fourier Transformation matrix by truncation of values from the proposed generic method which can help in computing DFT of varying lengths of vectors. On legacy computing machines and programming environments, having support for matrix multiplication, the proposed methodology can be implemented.

Supplementary and Associated Material

https://github.com/abdkhanstd/GSDFT: All codes and related data.

Keywords

Discrete Fourier Transform; Fourier Transform; Twiddle factor

Subject

MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics

Comments (1)

Comment 1
Received: 11 March 2022
Commenter: Abdullah Khan
Commenter's Conflict of Interests: Author
Comment: The following updates and changes have been incorporated:
1) Made some minor changes in the abstract.
2) Added experiments and results section along with two figures for results.
3) Added GitHub repository link.
4) Adjusted Equation (6) and (10).
5)Added a Conclusion.
6)Updated and added some references .
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