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[[Category:problem solving]]
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[[Category:ECE301]]
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[[Category:ECE]]
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[[Category:Fourier transform]]
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[[Category:inverse Fourier transform]]
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[[Category:signals and systems]]
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== Example of Computation of inverse Fourier transform (CT signals) ==
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A [[CT_Fourier_transform_practice_problems_list|practice problem on CT Fourier transform]]
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----
 
<math>X(\omega ) = \delta(\omega ) + \delta(\omega - 5) + \delta(\omega - 5)\,</math>
 
<math>X(\omega ) = \delta(\omega ) + \delta(\omega - 5) + \delta(\omega - 5)\,</math>
  
 
<math>x(t) = \int_{-\infty}^{\infty}X(\omega )e^{j\omega t}d\omega\,</math>
 
<math>x(t) = \int_{-\infty}^{\infty}X(\omega )e^{j\omega t}d\omega\,</math>
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<math> =  \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega )e^{j\omega t}d\omega + \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega - 5)e^{j\omega t}d\omega + \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega + 5)e^{j\omega t}d\omega\,</math>
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<math> = \frac{1}{2\pi}*1 + \frac{1}{2\pi}*e^{5jt} + \frac{1}{2\pi}*e^{-5jt}\,</math>
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<math> = \frac{1}{2\pi} * (1 + 2cos(5t))\,</math>
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I'll add another one when i have time
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----
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[[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]]

Latest revision as of 11:46, 16 September 2013

Example of Computation of inverse Fourier transform (CT signals)

A practice problem on CT Fourier transform


$ X(\omega ) = \delta(\omega ) + \delta(\omega - 5) + \delta(\omega - 5)\, $

$ x(t) = \int_{-\infty}^{\infty}X(\omega )e^{j\omega t}d\omega\, $

$ = \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega )e^{j\omega t}d\omega + \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega - 5)e^{j\omega t}d\omega + \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega + 5)e^{j\omega t}d\omega\, $

$ = \frac{1}{2\pi}*1 + \frac{1}{2\pi}*e^{5jt} + \frac{1}{2\pi}*e^{-5jt}\, $

$ = \frac{1}{2\pi} * (1 + 2cos(5t))\, $


I'll add another one when i have time


Back to Practice Problems on CT Fourier transform

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Questions/answers with a recent ECE grad

Ryne Rayburn