(New page: == Inverse F.T'ing == Given <math>X(\omega) = 3\pi\delta(\omega-\pi)+\delta(\omega-2\pi)-2\pi\delta(\omega-3\pi)\!</math> ____ <math>x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega...) |
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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]] | ||
| + | ---- | ||
| + | |||
== Inverse F.T'ing == | == Inverse F.T'ing == | ||
Given | Given | ||
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<math>x(t)= \frac{3*e^{j\pi*t}}{2}e^{jwt}+\frac{e^{j2\pi*t}}{2\pi}e^{jwt}-e^{j3*\pi*t}e^{jwt}</math> | <math>x(t)= \frac{3*e^{j\pi*t}}{2}e^{jwt}+\frac{e^{j2\pi*t}}{2\pi}e^{jwt}-e^{j3*\pi*t}e^{jwt}</math> | ||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:40, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
Inverse F.T'ing
Given
$ X(\omega) = 3\pi\delta(\omega-\pi)+\delta(\omega-2\pi)-2\pi\delta(\omega-3\pi)\! $
____
$ x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{jwt}dw $
$ x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}[3\pi\delta(\omega-\pi)+\delta(\omega-2\pi)-2\pi\delta(\omega-3\pi)\!]e^{jwt}dw $
$ x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}3\pi\delta(\omega-\pi)e^{jwt}dw+\frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega-2\pi)e^{jwt}dw-\frac{1}{2\pi}\int_{-\infty}^{\infty}2\pi\delta(\omega-3\pi)\!e^{jwt}dw $
$ x(t)= \frac{3}{2}\int_{-\infty}^{\infty}\delta(\omega-\pi)e^{jwt}dw+\frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega-2\pi)e^{jwt}dw-\int_{-\infty}^{\infty}\delta(\omega-3\pi)\!e^{jwt}dw $
$ x(t)= \frac{3*e^{j\pi*t}}{2}e^{jwt}+\frac{e^{j2\pi*t}}{2\pi}e^{jwt}-e^{j3*\pi*t}e^{jwt} $
