TUKEY, An algorithm for the machine calculation of

complex Fourier series, Math.

For the complex Fourier series a 3D vector harmonic [x.sub.k] (t) [member of] [L.sup.(3).sub.2] (T) of the k-th order

Further let's suppose that the constant component in the complex Fourier series is absent ([X.sub.0] = 0)

The spectral analysis of the T-periodical energetic processes of the current and voltage is used their representation by the complex Fourier series

Tukey, "An algorithm for the machine calculation of

complex Fourier series", Mathematics of Computation, vol.

Tukey, "An algorithm for the machine calculation of

complex Fourier series," Mathematics of Computation, vol.

Mathematically, this unsteady forcing function due to the pinion is best described by a complex Fourier series with a fundamental frequency equal to the pinion rotational rate, [f.sub.r].

The Fourier transform of the complex Fourier series is a one-sided pure line spectrum at multiples of the gear rotation rate.

Then we can write the output voltage of the first branch in the form of a complex Fourier series [1], [4]:

The developed equations in the form of a complex Fourier series for each inverter connection are valid for any coefficient of modulation, frequency and voltage control coefficients.

The inverter's output voltage of the first branch can be mathematically expressed as a complex Fourier series of the form [3-6]

The method is based on use of complex Fourier series calculation.