Radar and Sonar Signal Design: Use of Stationary Phase Approximation
Technical publication Oct 1967-Oct 1968
NAVAL UNDERSEA RESEARCH AND DEVELOPMENT CENTER SAN DIEGO CA
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The stationary phase approximation of Woodwards time-frequency correlation function Chitau, beta is considered. It is shown, from the condition that the stationary points lie within the interval of integration, that there can be developed inequalities which specify those domains of the tau - beta plane, except for some small neighborhood of the origin, on which the ambiguity function the absolute value of Chitau, beta squared is relatively large. Some simple phase modulations phit are studied to illustrate the method and to serve as a basis for determining heuristically that appropriately placed finite discontinuities in the instantaneous frequency phit result in the displacement of a part of the ambiguity volume from within to beyond physically interesting values of beta. Finite discontinuities in the phase modulation itself do not matter in this respect, and the replacing of a finite jump in phit by a linear transition occurring in a sufficiently small interval is shown to have a negligible effect. Further, the undisplaced volume can be spread out in azimuth about the origin. It appears possible to approximate an ideal ambiguity function by thus distributing the total ambiguity volume.
- Acoustic Detection and Detectors
- Active and Passive Radar Detection and Equipment