3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we analytically derive familiar q-space metrics and introduce a novel hyperspherical diffusivity measure. ...

The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type weight function on the sphere. Their analysis is carried out by means of differential-difference operators. The symmetries of this system involve the Weyl group o...

ABSTRACT This paper presents a new algorithm for harmonic estimation in power systems. It utilizes separable least squares (SLS) technique to estimate the magnitude and phase angle of the harmonics by analyzing the waveform. As well as hybrid techniques have been utilized in this paper to estimate harmonics, real coded genetic algorithm (RCGA) and particle swarm optimization (PSO) utilized to e...

This paper investigates the acoustic noise radiated from two nominally identical induction motors when fed from sinusoidal, and asymmetric regular sampling subharmonic and space-vector pulsewidth modulation (PWM) converters. The theory for analyzing the noise spectrum is developed further to account for the interaction between the motor and the drive. It is shown that manufacturing tolerances c...

Harmonic pollution of double fed induction generators (DFIGs) has become a vital concern for its undesirable effects on power quality issues of wind generation systems and grid-connected system, and the double pulse width modulation (PWM)converter is one of the main harmonic sources in DFIGs. Thus the harmonic analysis of the converter in DFIGs is a necessary step to evaluate their harmonic pol...

It is well known that additional space harmonics in the air-gap magnetomotive force (MMF) distribution of the concentrated non-overlapping windings (CW) cause additional losses in the machine. This is especially so for machines used for traction applications where the machine requires to operate over its rated speed and frequency. In this paper, the authors investigates losses present in an int...

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . ...