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I'm doing some work on signals and power spectrums.

The book I am using says the spectrum for this light scattering signal is given by:

[tex]I(q,\omega ) = \frac{1}{{2\pi }}\int_{ - \infty }^\infty {\exp ( - i\omega t)} S(q,t)dt[/tex]

In the book an S term is given as:

[tex]S(q,t) = N\left\langle {{\gamma ^2}} \right\rangle \exp [ - ({q^2}{D_T} + 6{D_R})t][/tex]

So what I want to do is work out the spectrum manually (using mathemtica or matlab) and get the same answer that they do. I need this because soon I will be using equations that aernt in the book and need to make sure the spectrum comes out correct.

But when I try to do it in mathematic I get an error saying the integral does not converge.

Matlab gives an answer but it looks strange and wrong.

The book then says that the spectrum is therefore (this is what I want to arrive at via matlab or mathematica):

[tex]I(q,\omega ) = \frac{{N\left\langle {{\gamma ^2}} \right\rangle }}{\pi }\frac{{{q^2}{D_T} + 6{D_R}}}{{{\omega ^2} + {{({q^2}{D_T} + 6{D_R})}^2}}}[/tex]

any ideas?

Thanks