Statistically almost optimum nonlinear network design

The statistically-optimum unstable filter to separate desired signals from noise and other undesired signals is shown to take the form of a high gain amplifier, with several output channels, each one of which computes the best statistical measure of one of the signals or the noise. The sum of these outputs comprises a negative feedback circuit. The imposition of the requirement of stability on the overall system is shown to be the same as the imposition of stability on each component plus a small correction in the zero locations. The addition of nonlinear components follows from differences in the amplitude probability distributions. The methods of automatically compensating for the unalterable dynamic characteristics of the output device, of the high gain amplifier, and for changes in the ratio of signal to noise power, are shown. The information needed for this design is the power density spectrum or autocorrelation function of each signal and noise, and the amplitude probability distribution of each. The mechanics of the design are quite simple, and can be done with only a conventional knowledge of circuit theory. A new philosophy of statistically optimum systems is formulated, which embraces both linear and nonlinear systems, and eliminates the necessity of minimizing the error power.