Radar and Sonar Signal Design: Use of Stationary Phase Approximation
Abstract
The stationary phase approximation of Woodward's time-frequency correlation function Chi(tau, beta) is considered. It is shown, from the condition that the stationary point(s) 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 (Chi(tau, beta)) squared is relatively large. Some simple phase modulations phi(t) are studied to illustrate the method and to serve as a basis for determining heuristically that appropriately placed finite discontinuities in the instantaneous frequency phi'(t) 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 phi'(t) 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1970
- Accession Number
- AD0867198
Entities
People
- D. H. Hageman