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| + | [[Category:problem solving]] | ||
| + | [[Category:ECE301]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:Fourier transform]] | ||
| + | [[Category:inverse Fourier transform]] | ||
| + | [[Category:signals and systems]] | ||
| + | == Example of Computation of inverse Fourier transform (CT signals) == | ||
| + | A [[CT_Fourier_transform_practice_problems_list|practice problem on CT Fourier transform]] | ||
| + | ---- | ||
| + | |||
<math> X(w) = \frac{2sin{3(w-2\pi)}}{w-2\pi}\,</math><br><br> | <math> X(w) = \frac{2sin{3(w-2\pi)}}{w-2\pi}\,</math><br><br> | ||
We already knew that when <math> x(t) = \frac{sinWt}{\pi t}, X(w) = 1 for |w|<W. \,</math><br><br> | We already knew that when <math> x(t) = \frac{sinWt}{\pi t}, X(w) = 1 for |w|<W. \,</math><br><br> | ||
| − | <math> | + | when<math> x(t) = x(t-t_0), X(w) = e^{-jwt_0}X(jw)</math><br><br> |
W is 3 , and this was delayed <math>2\pi\,</math><br><br> | W is 3 , and this was delayed <math>2\pi\,</math><br><br> | ||
| + | |||
| + | So <math> x(t) = e^{j2\pi t} </math> for <math> |t| < 3 \,</math><br><br> | ||
| + | And <math> x(t) = 0 \,</math> for otherwise | ||
| + | |||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 11:49, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
$ X(w) = \frac{2sin{3(w-2\pi)}}{w-2\pi}\, $
We already knew that when $ x(t) = \frac{sinWt}{\pi t}, X(w) = 1 for |w|<W. \, $
when$ x(t) = x(t-t_0), X(w) = e^{-jwt_0}X(jw) $
W is 3 , and this was delayed $ 2\pi\, $
So $ x(t) = e^{j2\pi t} $ for $ |t| < 3 \, $
And $ x(t) = 0 \, $ for otherwise
