Thus far the treatment has focused on the description of random signals and their analyses, and how these signals are transformed by linear time-invariant systems. In this chapter we take a somewhat different approach; namely starting with what is known about input processes and of system requirements we look for an optimum system. This means that we are going to perform system synthesis. The approach achieves an optimal reception of information signals that are corrupted by noise. In this case the input process consists of two parts, the information bearing or data signal and noise, and we may wonder what the optimal receiver or processing looks like, subject to some criterion.
When designing an optimal system three items play a crucial role. These are:
In the following we briefly comment on these items: