AN EVALUATION OF A SIGNAL DISTORTION INTEGRAL.
NAVY UNDERWATER SOUND LAB NEW LONDON CONN
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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 Ht-tau J sub 1 Kthe square root of t squared - tau squaredthe 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
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