Errors in the demodulation algorithm with a generated carrier phase introduced by the low-pass filter

In this paper, we study the errors of the homodyne demodulation method based on arctangent function solutions (PGCATAN) which are associated with the use of a low-pass filter (LPF) in this signal phase demodulation algorithm. The method of demodulation of an interference signal by PGC-ATAN method is investigated in order to detect and consider in more detail the errors at the filtering stage (the article considers the moving average method), and corrections to the signal are analytically calculated, taking into account the error introduced by the low-pass filter. We obtained formulas for calculating corrections to the signals S1(t), S2(t), S3(t), S4(t) which received by filtering the original signal multiplied by the reference oscillator signal, the calculations were compared with the results of mathematical modeling of the interference signal processing by the PGC-ATAN method. The demodulation of the signal, taking into account the corrections, showed that, in general, the effect on the signal phase is small at a low heating rate, however, for high-speed processes, the error can lead to serious distortions of the desired signal phase. These calculated corrections for processed interference signal will improve the demodulation method based on the calculations of the arc tangent function and more accurately calculate the desired phase of the signal.