A new interpolation theorem with application to pulse transmission

An interpolation theorem is determined for the case when there are a finite number of arbitrarily placed sampling instants and the interpolation function is the output of a known filter. They are also the interpolation functions with the specified properties that have minimum energy. The theorem is used to determine the input to a communications channel given a finite number of samples of its output. This provides a generalization of matched filters and a perspective on the benefits of fractionally spaced equalization. The theorem is also used to construct masks of a family of pulses that are specified by the range of pulse voltages at a finite number of sampling instants. The theory determines how the pulse masks thus constructed is transformed when the pulse family is transmitted through a filter such as a length of transmission line