(→Inverse Fourier transform of X(w)) |
(→Specify a Fourier transform X(w)) |
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== Specify a Fourier transform <math>X(w)</math> == | == Specify a Fourier transform <math>X(w)</math> == | ||
| − | :<math> X(w)=2\pi \delta\left ( w- \frac{\pi}{4}\right ) </math> | + | :<math> X(w)=2\pi \delta\left ( w- \frac{\pi}{4}\right )+2\pi \delta\left ( w+ \frac{\pi}{4}\right ) </math> |
== Inverse Fourier transform of <math>X(w)</math>== | == Inverse Fourier transform of <math>X(w)</math>== | ||
Revision as of 18:59, 8 October 2008
Specify a Fourier transform $ X(w) $
- $ X(w)=2\pi \delta\left ( w- \frac{\pi}{4}\right )+2\pi \delta\left ( w+ \frac{\pi}{4}\right ) $
Inverse Fourier transform of $ X(w) $
- $ \begin{align} x(t)&=\frac{1}{2\pi}\int_{-\infty}^{\infty}X( \omega)e^{j\omega t}d\omega \\& =\frac{1}{2\pi}\int_{-\infty}^{\infty}2\pi \delta\left ( w- \frac{\pi}{4}\right )e^{j\omega t}d\omega \end{align} $
