Related papers: Fast algorithm of adaptive Fourier series
In the current work, a number of algorithms are developed and compared for the numerical solution of periodic (quasi-static) linear elastic mechanical boundary-value problems (BVPs) based on two different discretizations of Fourier series.…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
In this paper, we propose a novel Automatic and Scalable Face Detector (ASFD), which is based on a combination of neural architecture search techniques as well as a new loss design. First, we propose an automatic feature enhance module…
As a promising solution to boost the performance of distance-related algorithms (e.g., K-means and KNN), FPGA-based acceleration attracts lots of attention, but also comes with numerous challenges. In this work, we propose AccD, a…
In this paper, we study the impact of computational complexity on the throughput limits of the {\color{black}fast Fourier transform (FFT)} algorithm for {\color{black}orthogonal frequency division multiplexing(OFDM)} waveforms. Based on the…
Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years,…
Although Federated Learning has been widely studied in recent years, there are still high overhead expenses in each communication round for large-scale models such as Vision Transformer. To lower the communication complexity, we propose a…
We propose a coded computing strategy and examine communication costs of coded computing algorithms to make distributed Fast Fourier Transform (FFT) resilient to errors during the computation. We apply maximum distance separable (MDS) codes…
First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…
Robust fine-tuning aims to achieve competitive in-distribution (ID) performance while maintaining the out-of-distribution (OOD) robustness of a pre-trained model when transferring it to a downstream task. Recently, projected gradient…
Optimal selection of a subset of items from a given set is a hard problem that requires combinatorial optimization. In this paper, we propose a subset selection algorithm that is trainable with gradient-based methods yet achieves…
Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general,…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and…
This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…
A generic fast method for object classification is proposed. In addition, a method for dimensional reduction is presented. The presented algorithms have been applied to real-world data from chip fabrication successfully to the task of…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
Fourier-domain Difference Map (FDM) for phase retrieval with two oversampled coded diffraction patterns are proposed. FDM is a 3-parameter family of fixed point algorithms including Fourier-domain Hybrid-Projection-Reflection (FHPR) and…
In this paper, a new fast and low complexity transform is introduced for orthogonal frequency division multiplexing (OFDM) wireless systems. The new transform combines the effects of fast complex-Walsh-Hadamard transform (CHT) and the fast…