New results on pulsed-beam wavelets

Gerald Kaiser

doi:10.1117/12.342935

22 March 1999 New results on pulsed-beam wavelets

Gerald Kaiser

Proceedings Volume 3723, Wavelet Applications VI; (1999) https://doi.org/10.1117/12.342935
Event: AeroSense '99, 1999, Orlando, FL, United States

Abstract

Pulsed-Beam Wavelets are exact, causal solutions of the inhomogeneous wave equation or Maxwell's equations whose `wavelet parameters,' instead of giving a time and scale, specify the point of emission, launch time, the radius of the emitting aperture, direction of propagation, duration, and width of the pulse. We derive their far fields and time- domain radiation patterns and confirm that the beams can be made arbitrarily well focused by choosing the wavelet parameters accordingly. We also find the source distribution as a generalized function supported on the compact source region determined by the wavelet parameters. As the radius of the disk shrinks to zero, the distribution reduces to the usual point source represented by the causal Green function. It is suggested that such `physical wavelets' may be synthesized in practice.

Citation Download Citation

Gerald Kaiser "New results on pulsed-beam wavelets", Proc. SPIE 3723, Wavelet Applications VI, (22 March 1999); https://doi.org/10.1117/12.342935

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