Analytic signals and zero-locus in multiplexing systems



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The theory of analytic functions is used as a new approach to the study of conventional multiplexing schemes. The multiplexing process involves double and triple modulation techniques. The most general form of modulated waves exhibit simultaneous phase and envelope fluctuation. Phase and envelope relationships described in mathematical formulation have a strong dependence on the real and complex zeroes of the actual wave. The properties of analytic signals are studied, yielding a general theory of zero-representation of the original signal that contains its informational attributes. The mathematical representation of zeroes of a periodic real signal has physical significance when related to the spectra, phase, and envelope fluctuations. The zero-pattern representation offers the advantage of showing the phase envelope fluctuation in the time domain, and a frequency domain representation can be based on the frequency spectrum given by the Fourier series coefficient. [...]