Fundamental Aspects of Linear Multiplexing

A linear multiplex system is defined as one in which the separation of signals belonging to different channels is achieved by the use of linear, time-variant or time-invariant, filters. It is shown that a fundamental property of such systems is that the sets of signals associated with their respective channels are linear and disjoint. Conversely, signals that belong to linear and disjoint sets can be transmitted simultaneously and separated at the receiving end by means of linear, generally time-variant, filters. It is shown that frequency-band compression cannot be achieved with a linear system. In geometrical terms, the extraction of signals belonging to a specified channel may be regarded as the projection of the signal space on the manifold corresponding to the channel in question along a complementary manifold. The filtering process is formulated in analytical terms via the λ-domain technique. Methods of synthesizing linear multiplex systems of other than the conventional frequency- or time-division types are indicated.