A classical problem in radar theory is the detection of moving targets in a ground clutter plus receiver noise background. Improvements in clutter rejection have recently been made by replacing analog MTI processors by their digital equivalents as this eliminates many of the problems associated with the maintenance of the analog hardware. In an attempt to determine the ultimate improvements possible using this new technology, the MTI problem was formulated as a classical detection problem and solved using the generalized likelihood ratio test. By manipulating the likelihood ratio, the receiver could be interpreted as a clutter filter in cascade with a Doppler filter bank. The performance of the optimum receiver was evaluated in terms of the output signal-to-interference ratio and compared with well-known MTI processors. It was shown that near-optimum performance can be obtained using a sliding weighted Discrete Fourier Transform (DFT). All of the results in Part I assume uniformly spaced transmitted pulses, which, for high velocity aircraft, leads to aliasing of the target and clutter spectra and detection blind speeds. In Part II the maximum likelihood method is applied using a more general model for the non-uniformly sampled target returns. This leads to an optimum receiver that is a slightly more complicated version of the sliding weighted DFT. In addition to removing the detection blind speeds, it is found that unambiguous Doppler measurements