Signal dependent degradation in noise performance of optimum detectors for multiple signal detection

The detection of multiple signals in the presence of additive noise is addressed, and finite impulse response (FIR) filters are treated as arrays (or vectors) to facilitate mathematical manipulations. The problem is to find the filter coefficients such that the output is (i) indicative of the class of the input image, (ii) tolerant to additive input noise, and (iii) invariant to image distortions. The filter synthesis procedure is reviewed. Degradation in processor performance and the rise in output variance as the number of signals to be detected increases are discussed. It is shown that the variance is a nondecreasing function of the number of signals. Recursive expressions for the exact output variance and incremental changes in variance are derived