(New page: <math>x(t)=t^3 e^{-3t} </math> <math>X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt}</math> <math>= \int^{\infty}_{- \infty} t^3 e^{-3t} e^{-jwt}</math> <math>= \int^{\infty}_{- \infty} t^3...) |
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| − | <math>x(t)= | + | [[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]] | ||
| + | ---- | ||
| + | <math>x(t)=e^{-3t} u(t-3) u(t+3) </math> | ||
| − | <math>X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt}</math> | + | <math>X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt} dt</math> |
| − | <math>= \int^{\infty}_{- \infty} | + | <math>= \int^{\infty}_{- \infty} e^{-3t} u(t-3) u(t+3) e^{-jwt} dt</math> |
| − | <math>= \int^{ | + | <math>= \int^{3}_{-3} e^{-(3 + jw)t} dt</math> |
| − | <math>\frac{ | + | <math>[\frac{e^{-(3 + jw)t}}{-(3 + jw)}]_{-3}^{3}</math> |
| + | |||
| + | <math>\frac{e^{-(9 + 3jw)}}{-(3 + jw)} - \frac{e^{(9 + 3jw)}}{-(3 + jw)}</math> | ||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 11:27, 16 September 2013
Example of Computation of Fourier transform of a CT SIGNAL
A practice problem on CT Fourier transform
$ x(t)=e^{-3t} u(t-3) u(t+3) $
$ X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt} dt $
$ = \int^{\infty}_{- \infty} e^{-3t} u(t-3) u(t+3) e^{-jwt} dt $
$ = \int^{3}_{-3} e^{-(3 + jw)t} dt $
$ [\frac{e^{-(3 + jw)t}}{-(3 + jw)}]_{-3}^{3} $
$ \frac{e^{-(9 + 3jw)}}{-(3 + jw)} - \frac{e^{(9 + 3jw)}}{-(3 + jw)} $
