Related papers: The Sliding Window Discrete Fourier Transform
We introduce the Latent Fourier Transform (LatentFT), a framework that provides novel frequency-domain controls for generative music models. LatentFT combines a diffusion autoencoder with a latent-space Fourier transform to separate musical…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
We address the problem of recovering a signal (up to global phase) from its short-time Fourier transform (STFT) magnitude measurements. This problem arises in several applications, including optical imaging and speech processing. In this…
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…
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
New time-series analysis tools are needed in disciplines as diverse as astronomy, economics and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data.…
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…
Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground state properties of extended materials. The computational complexity of describing the Kohn-Sham orbitals is replaced by introducing a set of random…
In this paper, we present SSDNet, a novel deep learning approach for time series forecasting. SSDNet combines the Transformer architecture with state space models to provide probabilistic and interpretable forecasts, including trend and…
Recently, a Monte Carlo approach was proposed for processing highly redundant continuous frames. In this paper we present and analyze applications of this new theory. The computational complexity of the Monte Carlo method relies on the…
In many processes, the variations in underlying characteristics can be approximated by noisy multi-periodic patterns. If large-scale patterns are superimposed by a noise with long-range correlations, the detection of multi-periodic patterns…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
Although Transformer-based methods have significantly improved state-of-the-art results for long-term series forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series…
Time series forecasting remains a critical challenge across various domains, often complicated by high-dimensional data and long-term dependencies. This paper presents a novel transformer architecture for time series forecasting,…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
In order to enhance the performance of Transformer models for long-term multivariate forecasting while minimizing computational demands, this paper introduces the Joint Time-Frequency Domain Transformer (JTFT). JTFT combines time and…
We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…