Exact and approximate filtering in signal detection: An example (Corresp.)

The innovations approach in communication theory solves the signal detection problem in terms of a related nonlinear filter. Simulation data is presented which shows that, at least for one example, using the appropriate linear filter instead results in a very small loss of detection power even though the variance of the linear filter is considerably greater than that of the nonlinear one. The results also illuminate the role of "predictable processes" in communication theory.