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The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…
The Fast Fourier Transform (FFT) is a computationally intensive digital signal processing (DSP) function widely used in applications such as imaging, software-defined radio, wireless communication, instrumentation. In this paper, a…
Diffusion Transformer (DiT), an emerging diffusion model for image generation, has demonstrated superior performance but suffers from substantial computational costs. Our investigations reveal that these costs stem from the static inference…
Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular,…
Feature Transformation is crucial for classic machine learning that aims to generate feature combinations to enhance the performance of downstream tasks from a data-centric perspective. Current methodologies, such as manual expert-driven…
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…
Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
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…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
With growing deployment of Internet of Things (IoT) and machine learning (ML) applications, which need to leverage computation on edge and cloud resources, it is important to develop algorithms and tools to place these distributed…
GPU-based fast Fourier transform (FFT) is extremely important for scientific computing and signal processing. However, we find the inefficiency of existing FFT libraries and the absence of fault tolerance against soft error. To address…
We present StochasticPrograms.jl, a user-friendly and powerful open-source framework for stochastic programming written in the Julia language. The framework includes both modeling tools and structure-exploiting optimization algorithms.…
Image computation is a fundamental tool for performance assessment of astronomical instrumentation, usually implemented by Fourier transform techniques. We review the numerical implementation, evaluating a direct implementation of the…
There has been considerable research into improving Fast Fourier Transform (FFT) performance through parallelization and optimization for specialized hardware. However, even with those advancements, processing of very large files, over 1TB…
The Fast Fourier Transform (FFT), as a core computation in a wide range of scientific applications, is increasingly threatened by reliability issues. In this paper, we introduce TurboFFT, a high-performance FFT implementation equipped with…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
Massively parallel Fourier transforms are widely used in computational sciences, and specifically in computational fluid dynamics which involves unbounded Poisson problems. In practice the latter is usually the most time-consuming operation…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
The Discrete Fourier Transform (DFT) is essential for various applications ranging from signal processing to convolution and polynomial multiplication. The groundbreaking Fast Fourier Transform (FFT) algorithm reduces DFT time complexity…