Toward a unified theory of modulation—Part II: Zero manipulation

Part I of this two-part paper began with a study of band-limited signals which exhibit simultaneous phase and envelope fluctuations. The real and complex zeros of such signals were shown to be crucial parameters, and a viewpoint was established wherein zeros are regarded as fundamental informational attributes of signals. In Part II, the concept of modulation as zero manipulation is developed. This concept allows one to manipulate the zeros of a signal (i.e., to modulate the signal) in any practically convenient manner provided that the original zeros can be recovered in a demodulation process. The major portion of Part II is an illustrated survey of modulation processes. Narrow-band processes are dealt with first. Both well-known techniques, such as AM and SSB, and unconventional techniques are classified and explained in terms of zero manipulations. Conventional and single-sided forms of angle modulation are studied next. The zero-manipulation concept provides insight into the nature of the redundancy in wide-band angle modulation and suggests why angle modulation is both noise resistant and inefficient as a coding process. The final portion of the paper shows that the zero-manipulation concept can be used constructively as well as interpretively. Two topics are discussed: angle coding via zero conjugation, and interpolation of binary signals.