相关论文: Fourier Techniques for Very Long Astrophysical Tim…

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…

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)…

This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…

In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…

While recent advancements in foundation models have significantly impacted machine learning, rigorous tests on the performance of time series foundation models (TSFMs) remain largely underexplored. This paper presents an empirical study…

We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…

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…

Analytic signals constitute a class of signals that are widely applied in time-frequency analysis such as extracting instantaneous frequency (IF) or phase derivative in the characterization of ultrashort laser pulse. The purpose of this…

Since many decades, there is a general perception in literature that the Fourier methods are not suitable for the analysis of nonlinear and nonstationary data. In this paper, we propose a Fourier Decomposition Method (FDM) and demonstrate…

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…

Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local…

A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…

Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…

Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…

Fourier transform spectroscopy (FTS) has been widely used in a variety of fields in research, industry, and medicine due to its high signal-to-noise ratio, simultaneous acquisition of signals in a broad spectrum, and versatility for…

Neural time-series analysis has traditionally focused on modeling data in the time domain, often with some approaches incorporating equivalent Fourier domain representations as auxiliary spectral features. In this work, we shift the main…

In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…

Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…