(The relationship between Fourier and Laplace transform)
(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 $

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood