Т.Ya. Shevgunov – Ph.D. (Eng.), Associate Professor,

Moscow Aviation Institute (National Research University)

E-mail: shevgunov@gmail.com

О.А. Guschina – Post-graduate Student,

Moscow Aviation Institute (National Research University) E-mail: busya_03@mail.ru

In this paper, the spectral representation of the periodic synchronous averaging is considered. The exact analytical expression which connects the coefficients of Fourier series of original continuous time signal with the discrete time Fourier trans-form of the averaged sampled version was obtained taking into consideration all the effects such as difference between the true and averaging periods, the attenuation and the leakage. The results of the numerical simulation are presented for the periodic train of pulses. The chosen example shows that the waveform of the recovered signal can significantly differ from one period of the original signal, despite rather a slight difference in values between the true and averaging periods. It was identified in the presented paper that the difference  between the original and averaged signals measured by means of relative mean square error raises if the total signal observation length increases while the other parameters remains fixed.

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