Synthesis of Modulation Filters

The subclass of time-variable linear networks is considered which contains time-invariant components as well as ideal modulators one of whose inputs is a fixed periodic or almost periodic signal (the control signal). Using the state-variable description of such systems, necessary and sufficient conditions are given for a time-variable impulse response to be realizable by this class of networks. Two realizations are given and shown to be equivalent, although the second one, called the general - path filter, has certain practical advantages due to the greater degree of freedom in selecting the natural modes of the time-invariant part of the realization.