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In the Fourier transform $\hat{f}=\int_{\mathbb{R}^n}f(x)\exp(-2\pi j w x)$. What is a value of $|\exp(-2\pi j w x)|$?

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1 Answer 1

If $w\in\mathbb{R}^n$ and $j$ is the imaginary unit (what I ussually call $i$), then $|e^{-2\,\pi\,j\,w\cdot x}|=1$.

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but, What are the intermediary steps please –  juaninf Oct 24 '12 at 12:40
    
by indentity of Euler I know that expresion is equal to $|\cos(-2\pi j w x)+\sin(-2\pi j w x)|$ –  juaninf Oct 24 '12 at 12:44
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@Juan Almost, by Euler you know that this is equal to $|\cos(-2\pi wx) + j\sin(-2\pi wx)| = (\cos^2 + \sin^2)^{1/2}\ldots$. –  martini Oct 24 '12 at 13:03
    
ok, understand thanks –  juaninf Oct 24 '12 at 13:05

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