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Frequency response function (FRF) measurements are widely used in Gravitational Wave (GW) detectors, e.g., for the design of controllers, calibrating signals and diagnostic problems with system dynamics. The aim of this paper is to present…
Diffusion tractography is routinely used to study white matter architecture and brain connectivity in vivo. A key step for successful tractography of neuronal tracts is the correct identification of tract directions in each voxel. Here we…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems.…
Rock properties are environment- and condition-dependent which render field-laboratory comparisons ambiguous for a number of known and unknown reasons that constitute the upscaling problem. Unknowns are first transformed into knowns in a…
Seismic waves generated by earthquakes consist of multiple phases that carry critical information about Earth's internal structure as they propagate through heterogeneous media. These phases provide constraints from different regions of the…
Fourier transform spectroscopy (FTS) has been widely used as an analytical tool for many applications in science and engineering. In this paper, we describe the operation principle and practical implementation of an FTS prototype. First,…
Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at…
Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style…
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…
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian.…
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…
State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…
In this work, we present a new technique for the decomposition of multivariate data, which we call Multivariate Fast Iterative Filtering (MvFIF) algorithm. We study its properties, proving rigorously that it converges in finite time when…
Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of…
We propose a new statistical test to identify non-stationary frequency-modulated stochastic processes from time series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from…
This paper presents a framework grounded in the theory of describing function (DF) and incremental-input DF to theoretically analyze the nonlinear oscillatory response of automated vehicles (AVs) car-following (CF) amidst traffic…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…
This study aimed to develop a virtual sensing algorithm of structural vibration for the real-time identification of unmeasured information. First, certain local point vibration responses (such as displacement and acceleration) are measured…
Detecting fast-moving objects, such as unmanned aerial vehicle (UAV), from event camera data is challenging due to the sparse, asynchronous nature of the input. Traditional Discrete Fourier Transforms (DFT) are effective at identifying…