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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]] | ||
| + | ---- | ||
| + | |||
Let x(t)= <math>cos(t)</math> | Let x(t)= <math>cos(t)</math> | ||
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<math>x(t)=\frac{1}{2\pi}cos (t)\int_{-\infty}^{\infty}e^{j\omega t}d\omega</math> | <math>x(t)=\frac{1}{2\pi}cos (t)\int_{-\infty}^{\infty}e^{j\omega t}d\omega</math> | ||
| − | <math>x(t)=\frac{1}{2\pi}cos (t){\left.\frac{e^{j\omega t}}{ | + | <math>x(t)=\frac{1}{2\pi}cos (t){\left.\frac{e^{j\omega t}}{jt}\right]_{-\infty}^{\infty}}</math> |
| + | |||
| + | <math>x(t)=\frac{1}{2j\pi t}cos (t){\left.e^{j\omega t}\right]_{-\infty}^{\infty}}</math> | ||
| + | |||
| + | |||
| + | ---- | ||
| + | [[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
Let x(t)= $ cos(t) $
Then
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega $
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}cos(t)e^{j\omega t}d\omega $
$ x(t)=\frac{1}{2\pi}cos (t)\int_{-\infty}^{\infty}e^{j\omega t}d\omega $
$ x(t)=\frac{1}{2\pi}cos (t){\left.\frac{e^{j\omega t}}{jt}\right]_{-\infty}^{\infty}} $
$ x(t)=\frac{1}{2j\pi t}cos (t){\left.e^{j\omega t}\right]_{-\infty}^{\infty}} $
