Related papers: Pipelined Parallel FFT Architecture
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…
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…
We present a parallel version of the well-known Split-Step Fourier method (SSF) for solving the Nonlinear Schr\"odinger equation, a mathematical model describing wave packet propagation in fiber optic lines. The algorithm is implemented…
The fast Fourier transform (FFT) is undoubtedly an essential primitive that has been applied in various fields of science and engineering. In this paper, we present a decomposition method for parallelization of multi-dimensional FFTs with…
Modern processors deliver higher throughput for lower-precision arithmetic than for higher-precision arithmetic. For matrix multiplication, the Ozaki scheme exploits this performance gap by splitting the inputs into lower-precision…
The Number Theoretic Transform (NTT) is a fundamental operation in privacy-preserving technologies, particularly within fully homomorphic encryption (FHE). The efficiency of NTT computation directly impacts the overall performance of FHE,…
To train modern large DNN models, pipeline parallelism has recently emerged, which distributes the model across GPUs and enables different devices to process different microbatches in pipeline. Earlier pipeline designs allow multiple…
This review article was first published in 2008 as chapter 11 in the book "Fast Fourier Transforms," edited by C. S. Burrus, for the Connexions project at Rice University, which is sadly no longer online. It gives a high-level overview of…
This paper presents a comprehensive exploration of Fast Fourier Transform (FFT) and linear convolution implementations, integrating both conventional methods and novel approaches leveraging the Bit Slicing Multiplier (BSM) technique. The…
The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…
The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…
Fourier ptychography has attracted a wide range of focus for its ability of large space-bandwidth-produce, and quantative phase measurement. It is a typical computational imaging technique which refers to optimizing both the imaging…
In recent years the computing landscape has seen an in- creasing shift towards specialized accelerators. Field pro- grammable gate arrays (FPGAs) are particularly promising as they offer significant performance and energy improvements…
FPGA-based hardware accelerators have received increasing attention mainly due to their ability to accelerate deep pipelined applications, thus resulting in higher computational performance and energy efficiency. Nevertheless, the amount of…
The transfer-matrix technique is a convenient way for studying strip lattices in the Potts model since the compu- tational costs depend just on the periodic part of the lattice and not on the whole. However, even when the cost is reduced,…
Large-scale floating-point matrix multiplication is a fundamental kernel in many scientific and engineering applications. Most existing work only focus on accelerating matrix multiplication on FPGA by adopting a linear systolic array. This…
Embedded system performances are bounded by power consumption. The trend is to offload greedy computations on hardware accelerators as GPU, Xeon Phi or FPGA. FPGA chips combine both flexibility of programmable chips and energy-efficiency of…
This paper presents a memory efficient, high throughput parallel lifting based running three dimensional discrete wavelet transform (3-D DWT) architecture. 3-D DWT is constructed by combining the two spatial and four temporal processors.…
In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…
Large foundation models are becoming ubiquitous, but training them from scratch is prohibitively expensive. Thus, efficiently adapting these powerful models to downstream tasks is increasingly important. In this paper, we study a principled…