(→Problem 2 Fourier Transfer) |
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<math> \chi(\omega) = \int_{-\infty}^\infty \cos{(\pi t)} e^{-j\omega t} dt </math> | <math> \chi(\omega) = \int_{-\infty}^\infty \cos{(\pi t)} e^{-j\omega t} dt </math> | ||
| − | <math> = \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t} dt} + \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t} dt} | + | <math> = \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t}e^{-j\omega t} dt} + \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t}e^{-j\omega t} dt} |
Revision as of 13:11, 8 October 2008
Problem 2 Fourier Transfer
$ x(t) = \cos{\pi t} $
$ F(x(t)) = \int_{-\infty}^\infty x(t) e^{-j\omega t}dt $
$ \chi(\omega) = \int_{-\infty}^\infty \cos{(\pi t)} e^{-j\omega t} dt $
$ \chi(\omega) = \int_{-\infty}^\infty \cos{(\pi t)} e^{-j\omega t} dt $
$ = \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t}e^{-j\omega t} dt} + \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t}e^{-j\omega t} dt} $
