(Inverse Fourier Transform)
 
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== Inverse Fourier Transform==
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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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The formula of the inverse transform is:
  
Suppose the signal is <math>e^{j2(\pi)t}</math>
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:<math>x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \,</math>
  
The formula of the inverse transform is:
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Suppose we have <math>2 \pi \delta(w - 2\pi)</math> (From the 'not so easy' question in class)
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Substituting that into the formula:
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:<math>x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \,</math>
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:<math>x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \,</math>
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:<math>x(t) = e^{j2 \pi t}\,</math>
  
:<math>x(t) = \frac{1}{2\pi}\,</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 12:45, 16 September 2013

Example of Computation of inverse Fourier transform (CT signals)

A practice problem on CT Fourier transform


The formula of the inverse transform is:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \, $

Suppose we have $ 2 \pi \delta(w - 2\pi) $ (From the 'not so easy' question in class)

Substituting that into the formula:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = e^{j2 \pi t}\, $

Back to Practice Problems on CT Fourier transform

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