Bandwidth-Conserving Independent Amplitude and Phase Modulation

Bandwidth-Conserving Independent Amplitude and Phase Modulation By B. F. LOGAN, Jr.* (Manuscript received March 26, 1982) Given two baseband signals /(f) and g(t), suitably restricted in amplitude and bandlimited to [X, and [~n, -X], 0 {t)}, bandlimited to [c - / , 3 c + / ] and [--(c + /?), --(c -- /?)], where /3 need be only sightly larger than n, 3 and such that /(f) and g(t) may be recovered by bandlimiting log A(t) and >(f), respectively. The restriction X > 0, i.e., that the baseband signals be bandpass, is not essential but it is a practical constraint in approximating the required operations. Also a modification is given for conserving bandwidth in case the signals /(f) andg(f) are of disparate bandwidths. I. I N T R O D U C T I O N Double-sideband amplitude modulation is wasteful of bandwidth, but it offers the advantage of envelope detection (with full carrier). A simple way to utilize the same bandwidth in transmitting two independent signals, f(t) a n d g ( f ) , is the so-called in-phase and quadrature modulation S(t) = fit)cos ct - g(f)sin ct, where synchronous demodulation is required to recover / and g. A modification that allows / to be recovered (approximately) by envelope detection is S2(t) = |1 + f(t)cos ct - £(f)sin ct * Bell Laboratories. °Copyright 1983, American Telephone & Telegraph Company. Photo reproduction for noncommercial use is permitted without payment of royalty provided that each reproduction is done without alteration and that the Journal reference and copyright notice are included on the first page.