Linear transformations of the ambiguity function

The radar ambiguity function is useful as a criterion of goodness for modulation signals used to discriminate the range and range-rate of point targets. It is often desirable to change existing ambiguity functions to meet new specifications of resolvability. One way of accomplishing this task is by using linear transformations of the ambiguity function. A review of the properties of ambiguity functions pertinent to the paper is included. Sufficient conditions for linear transformations to result in new ambiguity functions are presented in several forms. Then, necessary and sufficient conditions for kernels of the linear transformations to correspond to linear signal transformations are derived.