An algorithm for fast computation of the multiresolution discrete Fourier transform

TL;DR

This paper introduces a fast, parallelizable algorithm for computing the multiresolution discrete Fourier transform, significantly reducing computational complexity and enabling efficient implementation in software or hardware.

Contribution

The paper proposes a novel algorithm that improves the efficiency of multiresolution DFT calculations by leveraging vectorization and parallelization techniques.

Findings

Reduces computation time for multiresolution DFT

Enables parallel processing implementation

Uses matrix notation for clarity and hardware mapping

Abstract

The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and Sandler [10] and utilizes the vectorization of calculating process at each stage of the considered transformation. This allows for the use of a computational process parallelization and results in a reduction of computation time. In the description of the computational procedure, which describes the algorithm, we use the matrix notation. This notation enables to represent adequately the space-time structures of the implemented computational process and directly map these structures into the constructions of a high-level programming language or into a hardware realization space.