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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]] | ||
| + | ---- | ||
The formula of the inverse transform is: | The formula of the inverse transform is: | ||
:<math>x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \,</math> | :<math>x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \,</math> | ||
| + | |||
| + | Suppose we have <math>2 \pi \delta(w - 2\pi)</math> (From the 'not so easy' question in class) | ||
| + | |||
| + | Substituting that into the formula: | ||
| + | |||
| + | :<math>x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \,</math> | ||
| + | |||
| + | :<math>x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \,</math> | ||
| + | |||
| + | :<math>x(t) = e^{j2 \pi t}\,</math> | ||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 11:45, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
The formula of the inverse transform is:
- $ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \, $
Suppose we have $ 2 \pi \delta(w - 2\pi) $ (From the 'not so easy' question in class)
Substituting that into the formula:
- $ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \, $
- $ x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \, $
- $ x(t) = e^{j2 \pi t}\, $
