(New page: == Signal == <math> x(t) = e^{-2t} u(t) + e^{-5t} u(t-4) \!</math> == Fourier Transform == <math> X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} dt \!</math> <math> X(\omega) ...) |
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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]] | ||
| + | ---- | ||
| + | |||
== Signal == | == Signal == | ||
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<math> X(\omega) = \frac{1}{2+j\omega } + \frac{e^{-(20+4j\omega )}}{5+j\omega } \!</math> | <math> X(\omega) = \frac{1}{2+j\omega } + \frac{e^{-(20+4j\omega )}}{5+j\omega } \!</math> | ||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:28, 16 September 2013
Example of Computation of Fourier transform of a CT SIGNAL
A practice problem on CT Fourier transform
Signal
$ x(t) = e^{-2t} u(t) + e^{-5t} u(t-4) \! $
Fourier Transform
$ X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} dt \! $
$ X(\omega) = \int_{0}^{\infty} e^{-2t} e^{-j\omega t} dt + \int_{4}^{\infty} e^{-5t} e^{-j\omega t} dt \! $
$ X(\omega) = \int_{0}^{\infty} e^{-(2+j\omega )t} dt + \int_{4}^{\infty} e^{-(5+j\omega )t} dt \! $
$ X(\omega) = {\left. \frac{e^{-(2+j\omega )t}}{-(2+j\omega )} \right]^{\infty}_0 } + {\left. \frac{e^{-(5 + j\omega )t}}{-(5 +j\omega )} \right]^{\infty}_4 }\, $
$ X(\omega) = \frac{1}{2+j\omega } + \frac{e^{-(20+4j\omega )}}{5+j\omega } \! $
