AN EVALUATION OF A SIGNAL DISTORTION INTEGRAL.
Abstract
Using formal methods, R. R. Goodman has given an integral representation of the response due to an arbitrary signal from a point source in a constant gradient medium. A generalization of this integral, valid for L squared signals, is evaluated by showing that the Fourier transform of e to the power (-i omega tau the square root of (1-K squared omega squared)) minus e to the power (-1 omega) is -2 pi K tau H(t-tau) J sub 1 (K(the square root of (t squared - tau squared)/the square root of (t squared - tau squared), where H is the unit step function. The final result is expanded in a series that converges rapidly for small gradients (small K). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 21, 1968
- Accession Number
- AD0681013
Entities
People
- David H. Wood
Organizations
- Navy Underwater Sound Laboratory