Interreciprocity in linear periodically time-varying networks with sampled outputs

We consider a linear periodically time-varying (LPTV) network (varying with frequency fs) excited by an input x(t). We show (using frequency-domain arguments) that if its output is sampled at fs, one can find a linear time-invariant (LTI) filter, which, when excited by x(t) and output sampled at fs, yields the same sequence as the LPTV network. We then use Tellegen's theorem to demonstrate interreciprocity in LPTV networks with sampled outputs. This enables the determination of the equivalent LTI filters from multiple sources in the LPTV network to the sampled output, using just one time-domain simulation. A first-order continuous-time delta sigma modulator is used to illustrate the theory.