Figure 7.5 illustrates convolution of
which is the same as . When , we say that is a matched filter for .7.7 In this case, is matched to look for a ``dc component,'' and also zero-padded by a factor of . The zero-padding serves to simulate acyclic convolution using circular convolution. Note from Eq. (7.3) that the maximum is obtained in the convolution output at time 0 . This peak (the largest possible if all input signals are limited to in magnitude), indicates the matched filter has ``found'' the dc signal starting at time 0 . This peak would persist in the presence of some amount of noise and/or interference from other signals. Thus, matched filtering is useful for detecting known signals in the presence of noise and/or interference .