Digital comm. 2: Simple detectors and matched filters

In this lecture, we investigate the simple detector, i.e., a detector consisting of an LPF, sampler, and threshold device. We derive the probability of error of simple detector along with conditions on the optimal sampling time and threshold value. In the second part of the lecture, we discuss the motivation of using matched filters as an optimal receive filter. We derive the frequency response of the matched filter for general Gaussian noise (NWGN).