Evaluation of Integrals and Sums Involving (sin(Mx)/sin(X))n
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT
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The response of equispaced arrays, either linear, planar, or volumetric, to distributed spatial fields, typically encounters, integrals which involve the kernel sinMxsinx or its square. Since this kernel oscillates rather fast with x for large M and does not decay with x, numerical integration of such functions can be very time consuming. By resorting to Parsevals theorem, such integrals can be significantly simplified, requiring only the Fourier transform of the complementary part of the integrand. This procedure is investigated and applied to several typical examples programs for the examples are also included. Keywords Mathematical models, Mathematical equations, Integration, Summation, Sinc function, Array response, Fourier transform, Parsevals theorem, Fast Fourier transform, Equispaced array.
- Numerical Mathematics