Related papers: The Sliding Window Discrete Fourier Transform
Over the past few decades, many applications of physics-based simulations and data-driven techniques (including machine learning and deep learning) have emerged to analyze and predict solar flares. These approaches are pivotal in…
The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…
In the manufacturing process, sensor data collected from equipment is crucial for building predictive models to manage processes and improve productivity. However, in the field, it is challenging to gather sufficient data to build robust…
In this paper, we consider the uniqueness of STFT phase retrieval with two window functions. We show that a complex-valued locally integrable nonseparable signal is uniquely determined up to a global phase by phaseless samples of its short…
In this paper, we revisit the use of spectrograms in neural networks, by making the window length a continuous parameter optimizable by gradient descent instead of an empirically tuned integer-valued hyperparameter. The contribution is…
A spatio-temporal metasurface is proposed to decompose in real time the temporal frequencies of electromagnetic waves into spatial frequencies onto a two-dimensional plane. The metasurface is analyzed and demonstrated using Fourier…
Bandlimiting and timelimiting operators play a fundamental role in analyzing bandlimited signals that are approximately timelimited (or vice versa). In this paper, we consider a time-frequency (in the discrete Fourier transform (DFT)…
Time-series classification is an important domain of machine learning and a plethora of methods have been developed for the task. In comparison to existing approaches, this study presents a novel method which decomposes a time-series…
Forecasting El Nino is one of the greatest challenges of science. We show how intensive, large and accurate time series allow us to see through time. Our Discrete Chi-square Method (DCM) can detect arbitrary trend and signal(-s)…
In this paper, a novel and robust algorithm is proposed for adaptive beamforming based on the idea of reconstructing the autocorrelation sequence (ACS) of a random process from a set of measured data. This is obtained from the first column…
We propose a bootstrapping framework to quantify uncertainty in time-frequency representations (TFRs) generated by the short-time Fourier transform (STFT) and the STFT-based synchrosqueezing transform (SST) for oscillatory signals with…
In this paper, a new single-carrier waveform, called chirped discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM), is proposed for the sixth generation of communications. As the initial study on this…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
To address the complexity of financial time series, this paper proposes a forecasting model combining sliding window and variational mode decomposition (VMD) methods. Historical stock prices and relevant market indicators are used to…
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…
The short-time Fourier transform (STFT) is widely used to analyze the spectra of temporal signals that vary through time. Signals defined over graphs, due to their intrinsic complexity, exhibit large variations in their patterns. In this…
This work presents a new procedure to extract features of grey-level texture images based on the discrete Schroedinger transform. This is a non-linear transform where the image is mapped as the initial probability distribution of a wave…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
Speech emotion recognition is crucial to human-computer interaction. The temporal regions that represent different emotions scatter in different parts of the speech locally. Moreover, the temporal scales of important information may vary…
This paper focuses on a stochastic system identification problem: given time series observations of a stochastic differential equation (SDE) driven by L\'{e}vy $\alpha$-stable noise, estimate the SDE's drift field. For $\alpha$ in the…