Differences in Estimates of the Amplitude,Phase, and Frequency for Analytical and Complex Representations of a Gaussian Radio Pulse

Exact expressions are obtained for the representation of a Gaussian radio pulse by an analytical signal and quantitative estimates are derived for the difference in the instantaneous values of the amplitude, phase and frequency for complex and analytical representations of this signal. It is shown that for a fairly narrow-band signal both representations are equivalent from the point of view of estimates of the instantaneous values of the amplitude, phase and frequency, while for a broadband signal the differences may amount to tens of percent.