What is the Laplace transform of an ideal low pass filter?
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What is the Laplace transform of an ideal low pass filter?

 
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lucy
Guest
Posted: Wed Dec 14, 2005 1:16 am    Post subject: What is the Laplace transform of an ideal low pass filter? Reply with quote
I failed to integrate the exponential kernel against the sinc
function...

Does anybody know what is the Laplace transform of an ideal low pass
filter?

thanks
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Ingeniur
Guest
Posted: Thu Dec 15, 2005 1:16 am    Post subject: Re: What is the Laplace transform of an ideal low pass filte Reply with quote
"lucy" <losemind@yahoo.com> wrote in message
news:1134502603.115693.72580@g43g2000cwa.googlegroups.com...
Quote:
I failed to integrate the exponential kernel against the sinc
function...

Does anybody know what is the Laplace transform of an ideal low pass
filter?

thanks

It would be something like


(1-exp(-sT))/s

Ing
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Randy Yates
Guest
Posted: Fri Dec 16, 2005 1:16 am    Post subject: Re: What is the Laplace transform of an ideal low pass filte Reply with quote
lucy wrote:
Quote:
I failed to integrate the exponential kernel against the sinc
function...

Does anybody know what is the Laplace transform of an ideal low pass
filter?

Yes, many people know. People like Oppenheim, Manolakis, Bracewell,
et al. They put that information in these nice little containers called
"books." You should try one some time.

--RY
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Fred Marshall
Guest
Posted: Fri Dec 16, 2005 8:08 am    Post subject: Re: What is the Laplace transform of an ideal low pass filte Reply with quote
"lucy" <losemind@yahoo.com> wrote in message
news:1134502603.115693.72580@g43g2000cwa.googlegroups.com...
Quote:
I failed to integrate the exponential kernel against the sinc
function...

Does anybody know what is the Laplace transform of an ideal low pass
filter?

If you will admit the Bilateral Laplace Transform (which is also known as
the Complex Fourier Transform) then the answer is yes.

But the particular function you ask about simplifies so that the transform
becomes the ordinary Fourier Transform - for which there is no label using
"Laplace" that I know of .... because the Laplace Transform requires the
functions be causal and the impulse response of the ideal lowpass filter
isn't causal.

It revolves around the region of "t" being either from -infinity to
+infinity or from 0 to infinity (causal).
The pairs are:

Transform: t s
Complex Fourier and Bilateral Laplace -inf to +inf sigma + jw
ordinary Fourier -inf to +inf jw
ordinary Laplace 0 to +inf sigma + jw

Ideal lowpass filter:
-inf to +inf jw

Therefore......... ordinary Fourier.... or Bilateral Laplace with sigma=0 if
you will.

Fred
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