Abstract Through the intermediary of state‐variable equations, realization of an N‐path filter from a prescribed transfer function is obtained. An equivalence is found which shows how passive RC circuits incorporating time‐variable gyrators can be used to realize N‐path filters. It is also proved possible to realize any stable transfer function as an N‐path filter structure and that the system is insensitive to the frequency of the multiplying signals or the frequency of the gyration conductance. „Listen again to this. I have seen moonlight Sometimes the statues leaning over like reeds In the middle of living fruit, – the statues”︁[1,p. 95].

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.