The effects of spectral estimation on matched filter design

Moving-average matched filters (MAMF's) are a class of digital filters used to detect the presence of a known signal in noise. Designing matched filters requires knowledge of the structure of the signal and the noise. If the spectral density of the noise is not known or is changing with time its spectral characteristics must be estimated. Since spectral estimators derive their estimates from a random process realization, the estimates themselves are probabilistic in nature. The performance of MAMF's based on these estimates must, in turn, be distributed in a probabilistic sense.

This thesis investigates the performance of MAMF's designed on the basis of several different spectral estimators. Theoretical aspects of MAMF's and spectral estimators are reviewed and developed. A simulation system is used to exercise the spectral estimators and MAMF's and to provide comparative performance data. A graphical representation, using contour plots, is developed and can be used to predict the performance of a given MAMF/signal/spectral estimator combination.

Finally, several methods of generating MAMF's whose output performance is relatively insensitive (or robust) to the probabilistic variations caused by the spectral estimators are developed and evaluated. The latter incorporates knowledge of the empirical distribution of the particular spectral estimator used, as well as the freedom of manipulating the signal.