We review the relation between the radar ambiguity function and the ma
tched filter, and then introduce a geometric concept of the matched fi
lter as a slice of the ambiguity function along a frequency-shift line
. With the help of this geometric concept, the conventional matched fi
lter can be generalized to a time-varying matched filter, which is equ
ivalent to the optimum time-frequency correlator and can be implemente
d with wavelet transforms. The application of the optimum wavelet corr
elator to the inverse synthetic aperture radar is illustrated.