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Gate-Geology-and-Geophysics-2014-->View question

Asked On2017-07-06 10:21:11 by:Aparna-Dasgupta

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The Fourier transform and integral of the Dirac delta function respectively are
(A) 1 and 1

derivation of fourier transform for the dirac-delta impulse
Note that if the impulse is centered at t=0, then the Fourier transform is equal to 1 (i.e. a constant). This is a moment for reflection. The constant function, f(t)=1, is a function with no variation - there is an infinite amount of energy, but it is all contained within the d.c. term. Since the fourier transform evaluated at f=0, G(0), is the integral of the function. For f(t)=1, the integral is infinite, so it makes sense that the result should be infinite at f=0. And since the function f(t) has no variation, it should have no frequency components, so the fourier transform should be zero everywhere f does not equal 0. This last paragraph should be understood at an intuitive level.

Answerd on:2017-07-10 Answerd By:Amogh

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