Transformations for radar ambiguity functions
This investigation sheds new light on the area of radar ambiguity functions and their ability to improve signal design. The problem is approached from two directions. First, a number of signal transformations are presented along with their corresponding ambiguity functions. These include both linear transformations induced by processing the signal through a linear time-variant system and nonlinear transformations generated by functional transformations upon the signal. Three simple linear signal transformations are shown to generate the allowable class of linear transformations of the ambiguity plane for signals that have rational or entire functions as their spectra. Hence, for the class of time-limited signals the complete class is presented. It is proven that nonlinear transformations of the ambiguity plane are restricted to only unrealistic signals. Second, the ambiguity function is perturbed in a number of ways in an effort to improve some quality of the signal for radar purposes. To this end tests based upon existing theorems are developed to determine the applicability of any particular perturbation. The class of linear transformations of the ambiguity function are presented in two forms: for ambiguity functions given in analytic and in digital form.
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STATISTICAL DERIVATION OF THE AMBIGUITY
PROPERTIES AND FOURIER TRANSFORMS OF AMBIGUITY
TRANSFORMATIONS OF THE AMBIGUITY PLANE
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