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This note is a preliminary study of radar signals viewed as discretised nonlinear dynamical systems. Motivated by [Haykin and Li 1995], a class of recursively defined signals is introduced, and two specific examples are considered. It will be shown that such signals can exhibit complex dynamics in phase space. This means that they experience sensitive dependence on initial conditions. Using the Lyapunov spectrum, we determine the stability of these signals. We will also investigate whether such signals are of practical use in radar by examining their ambiguity functions.