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I am a neophyte in Discrete Fourier Transform and I am procticing with discrete Sine-transform.

Specifically I want to calculate $$ \mathcal{F}_s \lbrace x \cdot e^{-x^2} \rbrace = \int\limits_{0}^{\infty } x \cdot e^{-x^2} \cdot \sin\left(x\right)\, \mathrm{d}x

= \frac{1}{2} \pi^2 \omega e^{- \frac{1}{4} \pi^2 \omega^2} $$

I am using the FFTw library and with a 64 points I get a very poor result. Can anybody please help to improve it?

This is my C++ code, plot and numerical data are attached.

Thank you very much in advance

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# A Help with Discrete Sine Transform

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