Bandwidth-conserving independent amplitude and phase modulation

Given two baseband signals f(t) and g(t), suitably restricted in amplitude and bandlimited to [λ, μ] and [−μ, −λ], 0 < λ < μ < ∞, it is shown how to generate a carrier signal, s(t) = A(t) cos{ct + φ(t)}, bandlimited to [c − β, c + β] and [−(c + β), − (c − β)], where β need be only sightly larger than μ, and such that f(t) and g(t) may be recovered by bandlimiting log A(t) and (φ(t), respectively. The restriction λ > 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(t) and g(t) are of disparate bandwidths.