(→The relationship between Fourier and Laplace transform) |
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For s imaginary (i.e., <math>s=jw</math>), | For s imaginary (i.e., <math>s=jw</math>), | ||
| − | <math>X(jw)=</math> | + | <math>X(jw)=\int_{-\infty}^{\infty}x(t){e^{-jwt}}\, dt</math> |
Revision as of 16:42, 24 November 2008
The relationship between Fourier and Laplace transform
The continuous-time Fourier transform provides us with a representation for signals as linear combinations of complex exponentials of the form $ e^{st} $ with $ s=jw $.
For s imaginary (i.e., $ s=jw $), $ X(jw)=\int_{-\infty}^{\infty}x(t){e^{-jwt}}\, dt $
