(New page: <math>x(t) = u(t)\frac{d}{dt}cos(t-2\pi)</math> <math>X(\omega) = j\omega\int\limits_{-\infty}^{\infty} cos(t-2\pi)u(t)e^{-j\omega t}dt</math> <math>= j\omega\int\limits_{0}^{\inft...) |
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| + | [[Category:problem solving]] | ||
| + | [[Category:ECE301]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:Fourier transform]] | ||
| + | [[Category:signals and systems]] | ||
| + | == Example of Computation of Fourier transform of a CT SIGNAL == | ||
| + | A [[CT_Fourier_transform_practice_problems_list|practice problem on CT Fourier transform]] | ||
| + | ---- | ||
<math>x(t) = u(t)\frac{d}{dt}cos(t-2\pi)</math> | <math>x(t) = u(t)\frac{d}{dt}cos(t-2\pi)</math> | ||
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<math>= j\omega e^{-j\omega 2\pi} \int\limits_{0}^{\infty}frac{1}{2}(e^{j\tau} e^{-j\omega \tau}dt</math> | <math>= j\omega e^{-j\omega 2\pi} \int\limits_{0}^{\infty}frac{1}{2}(e^{j\tau} e^{-j\omega \tau}dt</math> | ||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 11:32, 16 September 2013
Example of Computation of Fourier transform of a CT SIGNAL
A practice problem on CT Fourier transform
$ x(t) = u(t)\frac{d}{dt}cos(t-2\pi) $
$ X(\omega) = j\omega\int\limits_{-\infty}^{\infty} cos(t-2\pi)u(t)e^{-j\omega t}dt $
$ = j\omega\int\limits_{0}^{\infty} cos(t-2\pi)e^{-j\omega t}dt $
$ \tau = t - 2\pi $
$ = j\omega\int\limits_{0}^{\infty} cos(\tau)e^{-j\omega(\tau -2\pi)}dt $
$ = j\omega\int\limits_{0}^{\infty} cos(\tau)e^{-j\omega \tau}e^{-j\omega 2\pi}dt $
$ = j\omega e^{-j\omega 2\pi} \int\limits_{0}^{\infty} cos(\tau)e^{-j\omega \tau}dt $
$ = j\omega e^{-j\omega 2\pi} \int\limits_{0}^{\infty}frac{1}{2}(e^{j\tau} e^{-j\omega \tau}dt $
