## The concept of an optimum (matched) filter

#### It is prudent to ask the question: 'What type of averaging filter will give the best S/N ratio at the sampling point?' The answer is that it depends entirely on the symbol shape being used. Consider the two symbol shapes shown here, one a square (unshaped pulse) and the other a rounded pulse. For the square pulse, the S/N ratio at each point in the symbol is approximately constant, and an averaging process that gives equal weight to each point would be optimum. This in fact is exactly what an integrate and dump filter does. For the rounded pulse, however, it is evident that the S/N ratio is greater in the centre of the pulse than at the edges, and it would thus make sense to give more weight to averaging the central region rather than the edges of the symbol. Hence the integrate and dump filter would not be optimum for this shape of symbol. #### A detection filter that does optimize the S/N ratio for a symbol is called a matched filter because its averaging effect is matched to the pulse shape. The integrate and dump filter is thus a matched filter for a rectangular pulse shape, but would not be matched to a root raised cosine pulse, for example. |