According to studies done by M. I. Trifonov, the form of the optimal detection template for an observer model with additive internal noise depends not only on the signal to be detected, but also on the internal-external noise ratio. The optimal detection template described by Trifonov\u27s theory indeed exhibited superior performance over the conventional matched filter template, but the mathematical procedure Trifonov proposed for proving his theory was insufficient. During the course of this thesis project, an extensive research was carried out to study Trifonov\u27s theory and its implications. As a result of this research, a new mathematical technique was developed to fully prove Trifonov\u27s theory. My contributions presented in this thesis also include the extension of the study to two dimensional signals and the Monte Carlo simulation experiments which were conducted to verify the mathematical theory. The experiment results were found to be in agreement with Trifonov\u27s theory
