Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven’s formula connecting ellipsoidal and sphero-conal harmonics is generalize...

5 Spherical Harmonics 7 5.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.1 Harmonic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

in this paper a novel hybrid algorithm for harmonics estimation in power systems is proposed. the estimation of the harmonic components is a nonlinear problem due to the nonlinearity of phase of sinusoids in distorted waveforms. most researchers implemented nonlinear methods to extract the harmonic parameters. however, nonlinear methods for amplitude estimation increase time of convergence. hen...

This paper presents application of parametric techniques (Estimation of signal parameter by rotational invariance techniques (ESPRIT), Root multiple signal classification (Root MUSIC)) for the estimation of harmonics/inter harmonics produced by wind generator under constant, variable rotor speed, load imbalance. Accuracy of estimation by parametric techniques is checked on synthetic signal as w...

Intermodulation and harmonics are important in frequency analysis of nonlinear systems. In neuron research, most investigations are taken in studying synchronization between the external stimuli and the output of neuron, but harmonics and intermodulation are often ignored. In this paper, harmonics and intermodulation of the subthreshold FitzHugh-Nagumo neuron are investigated and their magnitud...

electric arc furnace (eaf) is one of the largest loads in electric power systems. it is highly time varying and nonlinear. its reactive power variations cause voltage fluctuations in nearby system which is known as flicker. on the other hand the nonlinear voltage-current characteristic causes strong voltage and current harmonics in eaf. to this end flexible ac transmission systems (facts) techn...