On the basis of the coincident relation between a radar signal and a radar ambiguity function

an arbitrary bounded two-dimensional function of intergrable square is presented as a necessary and sufficient condition for radar ambiguity function. It is further pointed out that the condition is equivalent to the realizability condition given by Wilcox.When a desired function satisfies the sufficient condition （for example

the sloping Gaussian radar ambiguity function）

then the synthesis of ambiguity functions would reduce to the approximation of optimum radar signals. With proper choice of the ortho-normal bases

the problem of synthesizing an ideal radar ambiguity function can be completely solved. At the same time optimum radar signal generator and its corresponding matched filter can be constructed by a Laguerre network.