Theory of Analytic Modulation Systems

Abstract

A general theory of analytic modulation systems is developed where the transmitted signal is of the form σ(t) = Re {eiwctf(z(t))}. Here f(z) is an analytic function (modulation law), and z(t) = x(t) + iy(t) is the analytic baseband signal whose real part x(t) is a bounded bandlimited signal of spectral support [—Ω,Ω] which is assumed to have a bounded Hilbert transform y(t). It is shown for a large class of {z(t)} and modulation laws that z(t) may be recovered using a receiver incorporating the inverse function of f as a detector with appropriate pre‐ and post‐detection filtering. The theory also shows that in the procedure for factoring certain positive bandlimited signals, an approximate Hilbert transform operator (bandlimited) may be used. A related result is that signals subjected to logarithmic companding (one‐sided) and filtering may be recovered by a non‐iterative method.

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

“…2 stemming from these basic definitions and also the results in Ref. 3 pertaining especially to high-pass functions.…”

Characterization of the range of the Hilbert transform for bounded bandlimited signals and applications

“…Let f1 be the signal that was defined in (8). An example for an unbounded BMO(R)-signal is If1, which is plotted in Fig.…”

“…. " [8]. However, based on the abstract H 1 -BMO(R) duality theory it is possible to define the Hilbert transform for those signals.…”

“…For example, the "analytical signal", which was used by Dennis Gabor in his "Theory of Communication" [9], is based on the Hilbert transform. Further concepts in which the Hilbert transform is an integral part, are the instantaneous amplitude, phase, and frequency of a signal and the theory of modulation [8].…”

Realisierung eines verzerrungsarmen Open-Loop Klasse-D Audio-Verstärkers mit SB-ZePoC

“…Das SB-ZePoC-Verfahren (Streitenberger et al, 2000(Streitenberger et al, , 2001Streitenberger, 2005) basiert auf einem Spektraltheorem, welches Logan bei seiner Arbeit in Zusammenhang mit der Click-Modulation (Logan, 1978) aufstellte. Dieses Verfahren kann mithilfe der digitalen Signalverarbeitung implementiert werden und ist wie PNPWM frei von harmonischen und IMVerzerrungen.…”