相关论文: Detection of large-scale noisy multi-periodic patt…

In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT)…

We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…

Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…

This paper focuses on recognizing dialed numbers in a touch-tone telephone system based on the Dual Tone MultiFrequency (DTMF) signaling technique with analysis of stochastic aspects during the noise and random duration of characters. Each…

Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier waveform for high mobility communications, is introduced here. AFDM is based on discrete affine Fourier transform (DAFT), a generalization of discrete Fourier…

Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when…

The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a…

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…

In this work, we present two parallel algorithms for the large-scale discrete Fourier transform (DFT) on Tensor Processing Unit (TPU) clusters. The two parallel algorithms are associated with two formulations of DFT: one is based on the…

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…

In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…

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…

Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…

Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…

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…

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…

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…

Detecting fast-moving objects, such as unmanned aerial vehicle (UAV), from event camera data is challenging due to the sparse, asynchronous nature of the input. Traditional Discrete Fourier Transforms (DFT) are effective at identifying…

Many experiments, and in particular gravitational wave detectors, produce continuous streams of data whose frequency representations contain discrete, relatively narrowband coherent features at high amplitude. We discuss the application of…

To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the…