Related papers: Quaternion-Valued Single-Phase Model for Three-Pha…
For the first time quaternions have been used for real-time frequency estimation, where the multi-dimensional nature of quaternions allows for the full characterization of three-phase power systems. This is achieved through the use of…
Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering.…
A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as…
Quaternion models have been developed for both direction of arrival estimation and beamforming based on crossed-dipole arrays in the past. However, for almost all the models, especially for adaptive beamforming, the desired signal is still…
Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms…
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…
Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms…
Coordinate transformations significantly simplify power systems computations. Most notably, the classical Clarke and dq0 transformations are widely used in three-phase systems, as together they transform balanced abc quantities into…
Affordable and reliable electric power is fundamental to modern society and economy, with the Smart Grid becoming an increasingly important factor in power generation and distribution. In order to fully exploit it advantages, the analysis…
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…
Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for…
Coordinate transformations provide dimensional reduction benefits across power system analysis, electric machine modeling, and power electronic converter control. This paper introduces a novel transformation based on Geometric Algebra that…
The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with…
The main aim of this paper is to study quaternion phase retrieval (QPR), i.e., the recovery of quaternion signal from the magnitude of quaternion linear measurements. We show that all $d$-dimensional quaternion signals can be reconstructed…
Learning from data in the quaternion domain enables us to exploit internal dependencies of 4D signals and treating them as a single entity. One of the models that perfectly suits with quaternion-valued data processing is represented by 3D…
The concept of the analytic signal is extended from the case of a real signal with a complex analytic signal to a complex signal with a hypercomplex analytic signal (which we call a hyperanalytic signal) The hyperanalytic signal may be…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
While deep learning has received a surge of interest in a variety of fields in recent years, major deep learning models barely use complex numbers. However, speech, signal and audio data are naturally complex-valued after Fourier Transform,…
The proposed method introduces a parameter determination approach based on the minimum Fractal box dimension (FBD) of Variational Mode Decomposition (VMD) components, aiming to address the issue of manual determination of VMD decomposition…
We propose a method that identifies a mode of Rayleigh waves and separates it from body waves and from other modes, using quaternions to represent multi-component data. Being well known the abilities of quaternions to handle rotations in…