There is given a set ofnordered pairs of time functions (ri(t),xi;(t)). A networkNis to be designed, whose output isxi(t− τ) in response to inputri(t− τ). A solution is presented consisting ofnparallel branches, each with its own unique sampling function followed by a linear, time invariant network. The inputsri(i) must, however, be linearly independent. If so,Nis linear with respect to linear combinations of thenri(t). A general formula is found for the sensitivity of each response function to variations in the input signal. A slight modification gives a more general network, applicable to inputsrinot linearly independent. It is shown how to designNfor stochastic, stationary inputs so that it presentsndesired statistical weighting functions to theninputs.