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A primary goal in radar waveform design is to achieve a prescribed discrete time radar ambiguity function. Radar waveform design to meet a given ambiguity function specification is an important issue under the waveform diversity technology. Much of the development in this area is for continuous time signals. For the discrete time case, the sampling rate becomes an important design issue. On the one hand, too low of a sampling rate results in spectral aliasing, on the other hand, a sampling rate chosen higher than necessary increases the computational burden. We show in this project that aliased spectra, arising from sampling below the Nyquist rate, may be completely eliminated. We plot the effects of quantization noise and timing jitter for subjective evaluation.