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Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…

Numerical Analysis · Computer Science 2015-02-06 H. M. de Oliveira , R. J. Cintra , R. M. Campello de Souza

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…

Numerical Analysis · Mathematics 2017-06-12 Sami Merhi , Ruochuan Zhang , Mark A. Iwen , Andrew Christlieb

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…

Information Theory · Computer Science 2015-05-19 Xuebin Wu , Meghanad Wagh , Ning Chen , Zhiyuan Yan , Ying Wang

Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…

Numerical Analysis · Computer Science 2011-10-28 Zhengjun Cao , Xiao Fan

The Discrete Fourier Transform (DFT) is widely utilized for signal analysis but is plagued by spectral leakage, leading to inaccuracies in signal approximation. Window functions play a crucial role in mitigating spectral leakage by…

Signal Processing · Electrical Eng. & Systems 2023-12-27 Haichao Xu , Xingpao Suo

Recently, video classification attracts intensive research efforts. However, most existing works are based on framelevel visual features, which might fail to model the temporal information, e.g. characteristics accumulated along time. In…

Computer Vision and Pattern Recognition · Computer Science 2016-08-18 Haimin Zhang

Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…

Neural and Evolutionary Computing · Computer Science 2025-06-10 Raoof HojatJalali , Edmondo Trentin

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…

Signal Processing · Electrical Eng. & Systems 2024-12-31 Linbo Shang , Zhichao Zhang

In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator,…

Functional Analysis · Mathematics 2017-06-01 Asghar Rahimi , Niloufar Seddighi

The Discrete Fourier Transform (DFT) is a fundamental computational primitive, and the fastest known algorithm for computing the DFT is the FFT (Fast Fourier Transform) algorithm. One remarkable feature of FFT is the fact that its runtime…

Data Structures and Algorithms · Computer Science 2019-02-28 Michael Kapralov , Ameya Velingker , Amir Zandieh

Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style…

Systems and Control · Computer Science 2015-08-26 Hugh L. Kennedy

Frames have become standard tools in signal processing due to their robustness to transmission errors and their resilience to noise. Equiangular tight frames (ETFs) are particularly useful and have been shown to be optimal for transmission…

Information Theory · Computer Science 2016-12-06 Somantika Datta , Jesse Oldroyd

The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…

Data Structures and Algorithms · Computer Science 2024-12-18 Saulo Queiroz , João P. Vilela , Edmundo Monteiro

Channel estimation is one of the most important parts in current mobile communication systems. Among the huge contributions in channel estimation studies, the discrete Fourier transform (DFT)-based channel estimation has attracted lots of…

Information Theory · Computer Science 2015-04-29 H. Yu , C. Yang

In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point…

Computational Complexity · Computer Science 2025-12-23 Saulo Queiroz

Foundation models have achieved tremendous success in different domains. However, their huge computation and storage complexity make these models difficult to fine-tune and also less applicable in practice. Recent study shows training in…

Machine Learning · Computer Science 2025-07-16 Xinyu Ding , Lexuan Chen , Siyu Liao , Zhongfeng Wang

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…

Numerical Analysis · Mathematics 2025-06-09 Melanie Kircheis , Daniel Potts

This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…

Chaotic Dynamics · Physics 2007-05-23 Carlos R. Fadragas , Juan V. Lorenzo-Ginori , Ruben Orozco-Morales

The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms…

Quantum Physics · Physics 2022-03-21 Hsuan-Hao Lu , Navin B. Lingaraju , Daniel E. Leaird , Andrew M. Weiner , Joseph M. Lukens

A novel template matching algorithm that can incorporate the concept of deformable parts, is presented in this paper. Unlike the deformable part model (DPM) employed in object recognition, the proposed template-matching approach called…

Computer Vision and Pattern Recognition · Computer Science 2016-04-13 Hyungtae Lee , Heesung Kwon , Ryan M. Robinson , William D. Nothwang