Related papers: Complex Frequency as Generalized Eigenvalue
The letter provides a geometrical interpretation of frequency in electric circuits. According to this interpretation, the frequency is defined as a multivector with symmetric and antisymmetric components. The conventional definition of…
The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real…
The paper shows the equivalence between the geometric frequency of an electric quantity, namely, voltage and current, and the Lagrange derivative of a stream-line of a fluid. The geometric frequency is a concept recently proposed by the…
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…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
This paper presents exploratory investigations on the concept of generalized geometrical frequency in electrical systems with an arbitrary number of phases by using Geometric Algebra and Differential Geometry. By using the concept of…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…
This letter seeks to clarify the different existing definitions of both instantaneous complex phase and frequency as well as their equivalence under standard modeling assumptions considered for transmission systems, i.e. balanced positive…
Linear time-translation-invariant (LTI) models offer simple, yet powerful, abstractions of complex classical dynamical systems. Quantum versions of such models have so far relied on assumptions of Markovianity or an internal state-space…
This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the…
We describe a geometric method to quantify wave patterns observed in the nervous system, which are non-stationary and with a mixture of spiral, target, plane and irregular waves. The method analyzes fluctuations of the energy angular…
The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of…
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
This work investigates the multiplicity and differentiability of eigenfrequencies in structures with various symmetries. In particular, the study explores how the geometric and design variable symmetries affect the distribution of…
In this work we provide a mathematical framework to describe the periodically time variant (PTV) linear systems. We study their frequency-domain features to estimate the output bandwidth, a necessary value to obtain a suitable digital…