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The Carson and Fry (1937) introduced the concept of variable frequency as a generalization of the constant frequency. The instantaneous frequency (IF) is the time derivative of the instantaneous phase and it is well-defined only when this…
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 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…
Intrinsic Frequency (IF) has recently been introduced as an ample signal processing method for analyzing carotid and aortic pulse pressure tracings. The IF method has also been introduced as an effective approach for the analysis of…
One of the fundamental concerns in the operation of modern power systems is the assessment of their frequency stability in case of inertia-reduction induced by the large share of power electronic interfaced resources. Within this context,…
In previous work, we presented a general framework for instantaneous time-frequency analysis but did not provide any specific details of how to compute a particular instantaneous spectrum (IS). In this work, we use instantaneous…
The concept of complex frequency has been recently introduced on the IEEE Transactions on Power Systems to study bus voltage variations in magnitude and frequency and their link with complex power injections of a power system. In this…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
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…
This paper shows that the concept of complex frequency, originally introduced to characterize the dynamics of signals with complex values, constitutes a generalization of eigenvalues when applied to the states of linear time-invariant (LTI)…
We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time…
A novel mathematical framework is proposed to model Intersymbol Interference (ISI) phenomenon in wireless communication systems based on Orthogonal Frequency Division Multiplexing (OFDM) with or without cyclic prefix. The framework is based…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
This paper develops an instantaneous-frequency (IF) local estimator calculated with the complex Teager-Kaiser energy operator (CTKEO) and the dynamic-signal identity. The contribution is a novel IF expression that makes the…
This paper proposes a general framework to evaluate power system strength. The formulation features twelve indicators, grouped in three dynamical orders, that quantify the resistance of bus voltage phasors and their first and second order…
This paper introduces a general and flexible framework for F0 and aperiodicity (additive non periodic component) analysis, specifically intended for high-quality speech synthesis and modification applications. The proposed framework…
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…
Analysis of ac electrical systems can be performed via frame transformations in the time-domain or via harmonic transfer functions (HTFs) in the frequency-domain. The two approaches each have unique advantages but are hard to reconcile…
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…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…