The effect of increasing the sampling rate on the effectiveness of the matched filter

Matched filters are used when one would like to determine whether or not a particular, known waveform is present in a signal that has been corrupted by random noise. We show that in a sampled-data system, increasing the sampling rate only makes substantial improvements in the filter´s performance up to a certain point. Sampling very quickly turns out to be a waste of effort. The justification of this result makes use of the Perron-Frobenius theorem for positive, positive semi-definite matrices, and it makes use of the properties of totally positive matrices.