Related papers: Fourier Techniques for Very Long Astrophysical Tim…

Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…

An accurate treatment of electronic spectra in large systems with a technique such as time dependent density functional theory (TDDFT) is computationally challenging. Due to the Nyquist sampling theorem, direct real time simulations must be…

Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…

For supernovae gravitational wave signal analysis which intend to reconstruct supernova gravitational waves waveforms, we compare the performance of short-time Fourier transform (STFT), the synchroextracting transform (SET) and…

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…

We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in…

This paper explores the innovative application of the Fractional Fourier Transform (FrFT) in sound synthesis, highlighting its potential to redefine time-frequency analysis in audio processing. As an extension of the classical Fourier…

Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…

The detrended fluctuation analysis (DFA) is extensively useful in stochastic processes to unveil the long-term correlation. Here, we apply the DFA to point processes that mimick earthquake data. The point processes are synthesized by a…

The transformer model is known to be computationally demanding, and prohibitively costly for long sequences, as the self-attention module uses a quadratic time and space complexity with respect to sequence length. Many researchers have…

For the first time, complete source distributions for the emission and absorption of acoustic and electromagnetic wavelets are defined and computed, both in spacetime and Fourier space. The biggest surprise is the great simplicity of the…

We describe a method for spectral cleaning and timing calibration of short voltage time series data from individual radio interferometer receivers. It makes use of the phase differences in Fast Fourier Transform (FFT) spectra across antenna…

The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot…

The ability to detect anomalies in time series is considered highly valuable in numerous application domains. The sequential nature of time series objects is responsible for an additional feature complexity, ultimately requiring specialized…

Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…

In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…

Time-series forecasting is fundamental in industrial domains like manufacturing and smart factories. As systems evolve toward automation, models must operate on edge devices (e.g., PLCs, microcontrollers) with strict constraints on latency…

For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the…

As an old and widely used tool, it is still possible to find new insights and applications from Fast Fourier Transform (FFT)-based analyses. The FFT is frequently used to generate the Power Spectral Density (PSD) function, by squaring the…