Related papers: On Random Fields Associated with Analytic Wavelet …
The short-time Fourier transform (STFT) represents a window of audio samples as a set of complex coefficients. These are advantageously viewed as magnitudes and phases and the overall distribution of phases is very often assumed to be…
Applications of neural networks to condensed matter physics are becoming popular and beginning to be well accepted. Obtaining and representing the ground and excited state wave functions are examples of such applications. Another…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
Deep learning (DL) strategies have recently been utilized to diagnose motor faults by simply analyzing motor phase current signals, offering a less costly and non-intrusive alternative to vibration sensors. This research transforms these…
We develop methodology and theory for the detection of a phase transition in a time-series of high-dimensional random matrices. In the model we study, at each time point \( t = 1,2,\ldots \), we observe a deformed Wigner matrix \(…
In this work, time series analysis techniques are used to analyze sequential, equispaced mass measurements of a Si density artifact, collected from an electromechanical transducer. Specifically, techniques such as Power Spectral Density,…
The method of element analysis is proposed here as an alternative to traditional wavelet-based approaches to analyzing perturbations in financial signals by scale. In this method, the processes that generate oscillations in financial…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
Wavelets are waveform functions that describe transient and unstable variations, such as noises. In this work, we study the advantages of discrete and continuous wavelet transforms (DWT and CWT) of microlensing data to denoise them and…
Laser-plasma interferograms are currently analyzed by extracting the phase-shift map with FFT techniques (K.A.Nugent, Applied Optics {\bf 18}, 3101 (1985)). This methodology works well when interferograms are only marginally affected by…
Noise in various interferometer systems can sometimes couple non-linearly to create excess noise in the gravitational wave (GW) strain data. Third-order statistics, such as bicoherence and biphase, can identify these couplings and help…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display…
Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with…
We introduce a novel method for Additive Noise Analysis for Persistence Thresholding (ANAPT) which separates significant features in the sublevel set persistence diagram of a time series based on a statistics analysis of the persistence 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)…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
We present an analytic mean field theory for relaxational dynamics in spatially extended systems that undergo purely noise-induced phase transitions to ordered states. The theory augments the usual mean field approach with a Gaussian ansatz…
This note develops the first-ever noise-centric anomaly prediction method for a fused discrete-time signal. A Wavelet Packet Transform (WPT) provides a time--frequency expansion in which structure and residual can be separated via…