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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:signals and systems]]
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== Example of Computation of Fourier transform of a CT SIGNAL ==
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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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Let <font size = '4'><math>x(t) = e^{-a(t+1)} u(t + 1)</math></font>
 
Let <font size = '4'><math>x(t) = e^{-a(t+1)} u(t + 1)</math></font>
  
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<math>= -\frac{e^{-a}}{a+jw} [e^{-(a+jw)t}]^{\infty}_{1} </math>
 
<math>= -\frac{e^{-a}}{a+jw} [e^{-(a+jw)t}]^{\infty}_{1} </math>
  
<math>= -\frac{e^{-a}}{a+jw} [-e^{a+jw}]</math>
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<math>= -\frac{e^{-a}}{a+jw} [-e^{-(a+jw)}]</math>
  
 
<math>=\frac{e^{-(2a+jw)}}{a+jw}</math>
 
<math>=\frac{e^{-(2a+jw)}}{a+jw}</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 11:36, 16 September 2013

Example of Computation of Fourier transform of a CT SIGNAL

A practice problem on CT Fourier transform


Let $ x(t) = e^{-a(t+1)} u(t + 1) $

$ \chi(w) = \mathcal{F} (x(t)) = \int^{\infty}_{-\infty} e^{-at}e^{-a} u(t + 1) e^{-jwt} dt $

$ = e^{-a} \int^{\infty}_{-1} e^{-at}.e^{-jwt} dt $

$ = e^{-a} \int^{\infty}_{-1}e^{-(a+jw)t} dt $

$ = -\frac{e^{-a}}{a+jw} [e^{-(a+jw)t}]^{\infty}_{1} $

$ = -\frac{e^{-a}}{a+jw} [-e^{-(a+jw)}] $

$ =\frac{e^{-(2a+jw)}}{a+jw} $


Back to Practice Problems on CT Fourier transform

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Sees the importance of signal filtering in medical imaging

Dhruv Lamba, BSEE2010