Continuous-time envelope constrained filter design with input uncertainty

In envelope constrained (EC) filter design, the effect of input noise is mi nimized 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 res ponse of the optimal EC filter touches the output envelope, at some instanc es. Consequently, any disturbance in the prescribed input or implementation error could violate the output constraints. In an EC-filtering problem wit h uncertain input (ECUI), the set of possible inputs and the set of permiss ible outputs are defined by envelopes or masks. The objective is to design the filter to minimize the noise enhancement, while satisfying the constrai nt that every signal in the input envelope evokes a response, which stays i n the output envelope, This paper formulates the ECUI for analog filters, a nd presents a number of key results, which enable this problem to be solved .