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I have trouble with finding the Fourier Transform of the following function: $$ (t^2-1)^n(\operatorname{sign}(t-1)-\operatorname{sign}(t+1)), $$ where $n\in N$.

I know that the answer involve so called generalised sinc function, but I could not get the geneasl constant in front of the $\rm sinc(n, x).$

Thank you.

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