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I have to use Parseval's Theorem. I used it and ended with the integral of $(\operatorname{sinc}^2(kt))^2$. I know the Fourier Transform of $\operatorname{sinc}^2(kt)$ is the triangle function but I don't know how is the triangle function in frequency domain.

If someone can tell me how to solve this problem I will be grateful.

M Turgeon
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marina
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    Can you use the fact that the FT of a product is a convolution, and hence the answer here is the triangle function convoluted with itself? – anon Jun 15 '12 at 23:52
  • I don't think is enough with that. Right now I have the FT of sinc^2(kt) that is the triangle function. In other words the (triangle function)^2 but I don't know what "equation" to put in "triangle function" so I can evaluated the integral. – marina Jun 16 '12 at 00:08
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    The usual definition of a triangle waveform/function is the following: $$\Lambda(x)\equiv\begin{cases} 0 & \left|x\right|\geq1,\ 1-\left|x\right| & \left|x\right|<1. \end{cases}$$

    You can try to devide the problem into segments when doing your calculations, I mean, by looking at the convolution as a sliding of one triangle function onto another.

     – franckysnow Jun 16 '12 at 00:51
  • Still not get it. What do you mean with "at the convolution as a sliding of one triangle function onto another"? – marina Jun 16 '12 at 02:00
  • I think it would help if you would write down what you have done? You ended $\mathrm{sinc}^4(kt)$, but where did you start? – draks ... Jul 06 '12 at 19:27
  • https://see.stanford.edu/materials/lsoftaee261/PS-5-2007-Solutions.pdf Refer this site for detailed solution – Ashmika Dhabale Mar 14 '17 at 10:11

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