Are a Correlator and Its Matched Filter the Unique Optimal Sensors of a Known Signal in a White Noise Background?

摘要

The methods of generalized variational calculus are applied to design a set of spectral-time filters consisting of a multiplier for multiplying the input process by a known reference voltage and a stationary filter. Correlation reception and its matched filtering are shown to be particular limiting cases of the spectral-time filter, whose operation is explained in terms of the properties of the spectral correlation function. An example is given to illustrate how the noise immunity paradox can be resolved.