Latest revision as of 09:57, 15 September 2010

How to obtain the CT Fourier transform formula in terms of f in hertz (from the formula in terms of $ \omega $)

Recall:

$ \mathcal{X}(\omega )=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i2\pi ft} dt $

To obtain X(f), use the substitution

$ \omega= 2 \pi f $.

More specifically

$ \begin{align} X(f) &=\mathcal{X}(2\pi f)\\ &=\int_{-\infty}^{\infty} x(t) e^{-i2\pi ft} dt \end{align} $

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