Optimum pulse shape for minimum spectral occupancy in FSK signals

The characteristics of a frequency shift keying (FSK) signal giving rise to maximum power within a prescribed frequency band are determined. The baseband pulse shape extends over any integer number of bit periods. An integral equation for the optimum pulse shape is derived and some simple properties of the solution are investigated. The equation has been solved for some values of the product of the prescribed band times the pulse duration and the signal shape is shown. Our results for the particular case of pulses only one bit period long are presented for purpose of comparison with results known in the literature. Plots of out-of-band power for some values of the prescribed band and of pulse duration are reported. Finally a comparison with the well-known TFM, Nyquist, and raised cosine signals in terms of psdf and out-of-band power is exhibited.