A Spectral Theory for Hybrid Modulation

Certain properties of periodic signals are defined in terms of the zeros and singularities of associated analytic functions of a complex time variable
z
. This algebraic approach is a generalization of analytic signal theory, and leads to the conception of hybrid modulation as the superposition of two
z
-plane zero-singularity (ZS) patterns associated with amplitude- and angle-modulating signals, respectively. It is shown that important spectral properties of the modulated signal, such as band limitation, are explicit in the resultant pattern. Signal design is then interpreted in terms of ZS manipulation and placement. The theory is applied in a unified approach to compatible singlesideband (CSSB) modulation systems. It is shown that two types of proposed CSSB systems give rise to essentially nonband-limited output signals. The relation between conventional and single-sideband (SSB) angle modulation is also discussed in terms of their characteristic ZS patterns.