(→Problem 2 Fourier Transfer) |
|||
| (5 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
| + | [[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]] | ||
| + | ---- | ||
| + | |||
==Problem 2 Fourier Transfer== | ==Problem 2 Fourier Transfer== | ||
| − | <math> x(t) = \ | + | <math> x(t) = \cos{\pi t} </math> |
<math> F(x(t)) = \int_{-\infty}^\infty x(t) e^{-j\omega t}dt </math> | <math> F(x(t)) = \int_{-\infty}^\infty x(t) e^{-j\omega t}dt </math> | ||
| − | <math> \chi(\omega) = \int_{-\infty}^\infty \ | + | <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}e^{-j\omega t} dt} + \int_{-\infty}^\infty{ \frac{1}{2} e^{-j\pi t}e^{-j\omega t} dt} | ||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:30, 16 September 2013
Example of Computation of Fourier transform of a CT SIGNAL
A practice problem on CT Fourier transform
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} ---- [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] $
