  In previous work, we have argued that measurement using a radar can be viewed
as taking the expected value of an operator. The operator usually represents
some aspect of the characteristics of the object being tracked (such as
Doppler, distance, shape, polarization, etc.) that is measured by the radar
while the expectation is taken with respect to an optimal matched filter design
process based on the waveform broadcast by the radar and a receiver which is
optimized to a specific characteristic of the object being tracked. With
digital technology, it is possible to produce designer waveforms both to
broadcast and to mix with the return signal, so it is possible to determine the
maximum of the expectation of the operator by proper choice of the received
signal. We illustrate a method for selecting the choice of the return signal to
detect different "target operators" using perturbation theory based on the
Matched Filter Principle and illustrate it with different operators and
waveforms.
