In the case that the signal waveform possesses parameters, other than
the time of arrival that we wish to measure, then we must consider
a *bank* of filters,
(and
if there is
also an unknown phase), corresponding to a correlation of the
output with all of the possible signals
.
Here, the set of parameters is .
A set of statistics is then created according to the
methods given in the previous section. The largest of these statistics
is compared to the threshold to determine if a signal is present or
not. If it is decided that a signal is present, then the estimate
of the parameters of the signal are those parameters
corresponding to the largest statistic .

The filters in the filter bank will typically be densely packed into
the parameter space in order to accurately match any expected signal.
Thus, these filters will likely be highly correlated with one another.
To estimate the rate of false alarms, we appeal to the high threshold
limit in which each filter is effectively independent. Then, the
rate of false alarms is

(13.1.304) |

(13.1.305) |