(→Inverse Fourier Transform) |
|||
(3 intermediate revisions by one other user not shown) | |||
Line 1: | Line 1: | ||
− | == | + | [[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: | ||
− | + | :<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 12:45, 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}\, $