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I am confused between the difference between the Laplace transform and the Transfer function. I used to think that the Transfer Function was the Laplace transform of the Differential equation representation of a system, but in my readings it seems like that is incorrect - because according to my recent reading the transfer function is the laplace transform of the impulse response.

eg: say a system is defined such as:

[tex]\dot{y} + y = x[/tex]

the transfer function of this is:

[tex]H = \frac{1}{s+1}[/tex]

and this is obtained from a simple replacement of the derivatives with s.

so if I carry out inverse laplace transform of H, will it give me the impulse response of the system?

Also, on a side note, I am unclear on teh difference between the laplace and fourier transforms - what is the difference between them?

Thanks

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# Laplace Transform vs. Transfer Function

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