(New page: == Inverse Fourier Transform == <math> \chi(\omega) = 2\pi \sigma(\omega - \pi) <\math> <math> x[n] = frac{1}{2\pi}\int_{-\infty}^{\infty} \sigma(\omega-\pi)e^{j\omega t} dw </math> <m...) |
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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 Fourier Transform == | == Inverse Fourier Transform == | ||
| − | <math> \chi(\omega) = 2\pi \sigma(\omega - \pi) < | + | <math> \chi(\omega) = 2 \pi \sigma (\omega - \pi) </math> |
| − | <math> x[n] = frac{1}{2\pi}\int_{-\infty}^{\infty} \ | + | <math> x[n] = \frac{1}{2\pi}\int_{-\infty}^{\infty} 2\pi \delta (\omega - \pi)e^{j\omega t} dw </math> |
| − | <math> x[n] = \int_{-\infty}^\infty \ | + | <math> x[n] = \int_{-\infty}^\infty \delta (\omega - \pi)e^{j\omega t} dw </math> |
| + | |||
| + | <math> x[n] = \int_{\pi} e^{j\omega t} dw </math> | ||
| + | |||
| + | <math> x[n] = e^{j\pi t} </math> | ||
| + | |||
| + | ---- | ||
| + | [[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
Inverse Fourier Transform
$ \chi(\omega) = 2 \pi \sigma (\omega - \pi) $
$ x[n] = \frac{1}{2\pi}\int_{-\infty}^{\infty} 2\pi \delta (\omega - \pi)e^{j\omega t} dw $
$ x[n] = \int_{-\infty}^\infty \delta (\omega - \pi)e^{j\omega t} dw $
$ x[n] = \int_{\pi} e^{j\omega t} dw $
$ x[n] = e^{j\pi t} $
