Constrained Wiener filtering (Corresp.)

As is well-known, the introduction of causality conditions in Wiener filtering problems completely changes their solution. A constraint such as causality can be presented as a particular reduction of the observation space, and the constrained filter can always be obtained by projection onto this space. However, it is sometimes simpler to use an indirect method which gives the impulse response of the constrained filter by an appropriate modification of the unconstrained response. This method is presented and applied to many examples. In particular, the structure of constrained prediction filters is analyzed, and it is shown that the constrained innovation can be expressed in terms of the unconstrained one by an appropriate filter.