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The 3D Discrete Fourier Transform (DFT) is a technique used to solve problems in disparate fields. Nowadays, the commonly adopted implementation of the 3D-DFT is derived from the Fast Fourier Transform (FFT) algorithm. However, evidence…
Recent advances in high-resolution CT-imaging technology are creating a new class of ultra-high resolved micro-structural datasets that challenge the limits of traditional homogenization approaches. While state-of-the-art FFT-based…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
Large models represent a groundbreaking advancement in multiple application fields, enabling remarkable achievements across various tasks. However, their unprecedented scale comes with significant computational costs. These models, often…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…
Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…
The rise of deep learning has marked significant progress in fields such as computer vision, natural language processing, and medical imaging, primarily through the adaptation of pre-trained models for specific tasks. Traditional…
Vertex-frequency analysis, particularly the windowed graph Fourier transform (WGFT), is a significant challenge in graph signal processing. Tight frame theories is known for its low computational complexity in signal reconstruction, while…
We propose HHFT (Hierarchical Heterogeneous Feature Transformer), a Transformer-based architecture tailored for industrial CTR prediction. HHFT addresses the limitations of DNN through three key designs: (1) Semantic Feature Partitioning:…
This paper proposes a multivariable extremum seeking scheme using Fast Fourier Transform (FFT) for a network of subsystems working towards optimizing the sum of their local objectives, where the overall objective is the only available…
Field-Programmable Gate Arrays (FPGAs) have become essential in cloud computing due to their reconfigurability, energy efficiency, and ability to accelerate domain-specific workloads. As FPGA adoption grows, research into task scheduling…
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…
With the rapid growth in the use of fine-tuning for large language models (LLMs), optimizing fine-tuning while keeping inference efficient has become highly important. However, this is a challenging task as it requires improvements in all…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
Parallel algorithms relying on synchronous parallelization libraries often experience adverse performance due to global synchronization barriers. Asynchronous many-task runtimes offer task futurization capabilities that minimize or remove…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…