The cross ambiguity function (CAF) arises in many areas such as radar/sonar and communications when correlation processing is performed in the presence of a Doppler frequency shift. In this paper, the CAF synthesis problem is tackled: a pair of waveforms are jointly designed so that their CAF approximates a desired one. The so-generated waveforms have relatively low peak-to-average power ratios and in certain cases can be constant modulus. Numerical examples are provided to show the effectiveness of the proposed algorithm in synthesizing different types of CAF.