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In this paper, we study phase-amplitude multivariable dynamics in converter-based power systems from a complex-frequency perspective. Complex frequency represents the rate of change of voltage amplitude and phase angle by its real and…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed…
Representations of AC power systems by frequency dependent impedance equivalents is an emerging technique in the dynamic analysis of power systems including power electronic converters. The technique has been applied for decades in DC-power…
Expressing head-related transfer functions (HRTFs) in spherical harmonic (SH) domain has been thoroughly studied as a method of obtaining continuity over space. However, HRTFs are functions not only of direction but also of frequency. This…
Sensing via a mechanical frequency shift is a powerful measurement tool, and, therefore, understanding and mitigating frequency noise affecting mechanical resonators is imperative. Thermomechanical noise fundamentally limits mechanical…
In this paper, we present an analogy for a power system dominated by grid-forming (GFM) sources that proves to be a powerful visualization tool for analyses of power flow, frequency regulation, and power dispatch. Frequency droop…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
The presence of interharmonics in power systems can lead to asynchronous sampling, a phenomenon further aggravated by shifts in the fundamental frequency, which significantly degrades the accuracy of power measurements. Under such…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
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…
This paper proposes an efficient parameterization of the Room Transfer Function (RTF). Typically, the RTF rapidly varies with varying source and receiver positions, hence requires an impractical number of point to point measurements to…
Studying the coherence of an optical field is typically compartmentalized with respect to its different optical degrees of freedom (DoFs) -- spatial, temporal, and polarization. Although this traditional approach succeeds when the DoFs are…
The finite STFT Synchrosqueezing transform is a time-frequency analysis method that can decompose finite complex signals into time-varying oscillatory components. This representation is sparse and invertible, allowing recovery of the…
The Hamiltonian Mean Field (HMF) model of coupled inertial, Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by…
We present analytical and numerical results on the joint dynamics of two coupled Duffing oscillators with nonlinearity of opposite signs (hardening and softening). In particular, we focus on the existence and stability of synchronized…
Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by…
The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential…
This paper focuses on computing the frequency response and transfer functions for large self-similar networks under different circumstances. Modeling large scale systems is difficult due, typically, to the dimension of the problem, and…
Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…