| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
| + | [[Category:problem solving]] | ||
| + | [[Category:ECE301]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:Fourier transform]] | ||
| + | [[Category:signals and systems]] | ||
| + | == Example of Computation of Fourier transform of a CT SIGNAL == | ||
| + | A [[CT_Fourier_transform_practice_problems_list|practice problem on CT Fourier transform]] | ||
| + | ---- | ||
Specify a signal x(t) and compute its Fourier transform using the integral formula.( Make a hard one) | Specify a signal x(t) and compute its Fourier transform using the integral formula.( Make a hard one) | ||
| + | |||
| + | <math>e^{-2(t-1)}u(t-1)\,</math> | ||
<math>\,\mathcal{X}(\omega)=\int_{-\infty}^{\infty}x(t)e^{-j\omega t}\,dt\,</math> | <math>\,\mathcal{X}(\omega)=\int_{-\infty}^{\infty}x(t)e^{-j\omega t}\,dt\,</math> | ||
| + | |||
| + | <math>\,\mathcal{X}(\omega)= \int_{1}^{ \infty} e^{2-t(2+jw)}dt\,</math> | ||
| + | |||
| + | integrating and putting in limits | ||
| + | |||
| + | <math>\,\mathcal{X}(\omega)= \frac{e^{2-(2+jw)}}{2+jw} \,</math> | ||
| + | |||
| + | <math>\,\mathcal{X}(\omega)= \frac{e^{2-2-jw}}{2+jw} \,</math> | ||
| + | |||
| + | <math>\,\mathcal{X}(\omega)= \frac{e^{-jw}}{2+jw} \,</math> | ||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 11:24, 16 September 2013
Example of Computation of Fourier transform of a CT SIGNAL
A practice problem on CT Fourier transform
Specify a signal x(t) and compute its Fourier transform using the integral formula.( Make a hard one)
$ e^{-2(t-1)}u(t-1)\, $
$ \,\mathcal{X}(\omega)=\int_{-\infty}^{\infty}x(t)e^{-j\omega t}\,dt\, $
$ \,\mathcal{X}(\omega)= \int_{1}^{ \infty} e^{2-t(2+jw)}dt\, $
integrating and putting in limits
$ \,\mathcal{X}(\omega)= \frac{e^{2-(2+jw)}}{2+jw} \, $
$ \,\mathcal{X}(\omega)= \frac{e^{2-2-jw}}{2+jw} \, $
$ \,\mathcal{X}(\omega)= \frac{e^{-jw}}{2+jw} \, $
