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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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----
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For the signal:
 
For the signal:
  
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<math> x(t) = 1 + \frac{3}{2}e^{j3\pi t} - 2e^{-5\pi t}</math>
 
<math> x(t) = 1 + \frac{3}{2}e^{j3\pi t} - 2e^{-5\pi t}</math>
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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 12:50, 16 September 2013

Example of Computation of inverse Fourier transform (CT signals)

A practice problem on CT Fourier transform


For the signal:

$ X(\omega)= 2\pi \delta(\omega) + 3\pi \delta(\omega - 3\pi) - 4\pi \delta(\omega + 5\pi) $

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^\infty (2\pi \delta(\omega) + 3\pi \delta(\omega - 3\pi) - 4\pi \delta(\omega + 5\pi)) e^{j\omega t} \mathrm{d}\omega $

$ = \int_{-\infty}^\infty ( \delta(\omega) + \frac{3}{2} \delta(\omega - 3\pi) - 2 \delta(\omega + 5\pi)) e^{j\omega t} \mathrm{d}\omega $

$ x(t) = 1 + \frac{3}{2}e^{j3\pi t} - 2e^{-5\pi t} $



Back to Practice Problems on CT Fourier transform

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva