The representation of an electroencephalogram as a convolution of harmonic functions having negative decrements with discrete (evenly discontinuous) white Gaussian noise was considered. A substantiation of this representation is given. It was numerically shown that the convolution of the decrement damping alpha-rhythm of one frequency with discrete white noise is a narrow-band chaos, an irregular spindle-shaped activity, which results in the appearance of close spectral components in the spectrum of power. The estimation of the autocorrelation function represented a damping cosinusoid shifted in phase depending of the factor of fading. The absolute value of convolution described an envelope of the output signal. The average duration of spindles decreased as the module of the decrement increased.