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For various practical reasons, a highly desirable attribute of a realization procedure for the ambiguity function would be control over the envelope of the complex signal modulation. A design procedure is derived which has this property and begins with a specification of the range and Doppler cross sections of the ambiguity function. The essential problem is to find the phase modulation of the signal when the envelopes of the signal and its spectrum are specified; a solution is given for the large time-bandwidth product case. An application to the problem of avoiding range ambiguities is discussed.