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In this postWe are going to evaluate the Fourier transform of $\frac{\sin{x}}{x}$ and $\left(\frac{\sin{x}}{x}\right)^2$. And it turns out to be a comprehensive application of many elementary theorems of single complex variable functions. Thus it is recommended to make sure that you can evaluate and understand all the identities in this post by yourself. Also, make sure that you can recall what all words in italics means.Problem 1For real $t$, find the limit by\lim_{A \to \infty}\int_{-A}^{A}\fr...