Continuous-time envelope constrained filter design with input uncertainty

In envelope constrained (EC) filter design, the effect of input noise is minimized subject to the constraint that the filter's response to a specified signal fits into a prescribed envelope. It is always the case that the response of the optimal EC filter touches the output envelope, at some instances. Consequently, any disturbance in the prescribed input or implementation error could violate the output constraints. In an EC-filtering problem with uncertain input (ECUI), the set of possible inputs and the set of permissible outputs are defined by envelopes or masks. The objective is to design the filter to minimize the noise enhancement, while satisfying the constraint that every signal in the input envelope evokes a response, which stays in the output envelope. This paper formulates the ECUI for analog filters, and presents a number of key results, which enable this problem to be solved.