On the Peak Factor of Sampled and Continuous Signals

The peak factor of a continuous digitally- modulated signal is often analyzed from its samples taken at the Nyquist rate. This, however, may involve a significant error. It has been claimed, based on an illustrative example, that the peak factor of a continuous signal may be arbitrary large while the peak factor of the corresponding sampled signal is limited [Wulich, D., 2000]. A validity of this example has been questioned in [Ermolova, N., 2001; Minn, E., et al., 2001] based on a flaw in [Wulich, D., 2000]. In this paper, we demonstrate that the original illustrative example requires a small modification only to remove the flaw. It is also demonstrated that the continuous peak factor, in its traditional definition, may be arbitrary large while the sampled peak factor and the signal energy are bounded. An upper bound on the continuous peak factor of a BPSK sequence is derived.