Properties of Ambiguity Functions

The use of ambiguity functions in radar signal design and analysis is very common. Understanding the various properties and meanings of ambiguity functions allow a signal designer to understand the time delay and doppler shift properties of a given signal. Through the years, several different versions of the ambiguity function have been used. Each of these functions essentially have the same physical meaning; however, the use of different functions makes it difficult to be sure that certain properties hold for different formulations. This work proves several parallel properties of two versions of the asymmetric ambiguity function, the symmetric ambiguity function, and Woodwords original ambiguity function. It also provides some visualizations comparing the ambiguity functions for some common signals