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- Thread starter Poirot
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- Thread starter
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- Jan 26, 2012

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Let: \(g(x)=f'(x)\) and \(h(x)=g(a x)\), and \(H(\omega)\), \(G(\omega)\) and \(F(\omega)\) be the FT of \(h(x)\), \(g(x)\) and \(h(x)\) respectively.

then:

\[ H(\omega)=\frac{1}{a}G\left(\frac{\omega}{a}\right) \]

and:

\[ G(\omega) = i \omega F(\omega)\]

Now substitute the second into the first to get:

\[ H(\omega)=\frac{1}{a} \frac{ i \omega}{a}F\left(\frac{\omega}{a}\right) = \; \frac{i \omega}{a^2} F\left( \frac{\omega}{a}\right) \]

CB

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