Signals Designed for Recovery After Clipping-II. Fourier Transform Theory of Recovery

This paper develops a Fourier transform theory for the recovery of signals of a certain class from their zeros. The class, denoted by S(b, c), consists of real-valued signals of the form s(t) = g{t) + cos ct, where g is bandlimited to [−b, b], 0 < b < c < ∞, and such that (−1) k s(KΠ/c) > 0, which is satisfied, for example, if |g(t)| < 1. A very simple method of recovery is given for the case c > 3b, and a somewhat more complicated method is given for the case c > 2b. The theory also suggests a novel method of effecting amplitude modulation, which has advantages in high-power applications.