Two types of averaging techniques for target detection in a pulsed coherent lidar system were examined. The first, an FIR filter, results in a gamma distribution when used to average power spectra. The detection performance follows from the statistics of a gamma distribution. The second type of averaging technique, a first order IIR filter, is even simpler to implement and produces many of the same effects that the FIR filter does. While the distribution it produces does not precisely fit a gamma distribution, it can be approximated by a gamma distribution if the effective diversity is defined by N_(eff)=(1+α)/(1-α) (12) If this approximation is used, then the detection threshold and the asymptotic probability of detection are calculated in the same manner as with the FIR filter. The transient behavior of the IIR filter shows some differences from the transient behavior of the FIR filter. The IIR filter produces a higher probability of detection initially, but takes about twice as long to converge. In many lidar applications, there will be very little difference in performance between the FIR and IIR filter. The calculation of the detection threshold and the asymptotic probability of detection are essentially the same with either filter. The transient behavior shows some difference between the two but does not strongly favor one or the other. The IIR filter may be a more desirable choice (depending upon the application), simply because it is easier to implement.
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