# 3.5 Matched filtering

## Recovery of symbols from noise

#### Having dealt earlier with the issue of controlling the bandwidth of a data signal and filtering for minimum intersymbol interference we shall now turn our attention to the question of how to optimize the detection of data symbols in the presence of noise. This discussion will be limited to the case of Additive White Gaussian Noise which simplifies the mathematical treatment considerably. For many applications, this fortunately represents a good approximation to reality. |

#### Consider a binary symbol stream accompanied by noise entering the receiver. At some point during each symbol the receiver has to make a decision as to whether a 1 or 0 has been sent. The logical decision point is thus halfway between the two voltage levels representing each symbol.