Transient Response of Narrow-Band Networks to Narrow-Band Signals with Applications to Frequency Shift Keying

A method is presented for simplifying the calculation of transient response of narrow-band networks to narrow-band signals. Laplace transforms are used, but employ only positive frequencies, simplified by approximations justified by the narrowband properties of the networks and signals. The method is applied in calculating the transient response of 1- and 2-pole band-pass filters to a step change of frequency of a signal whose amplitude is constant. Curves are included, showing the instantaneous amplitude, phase, and frequency of the filter outputs.