Science > Physics > how to compute the laplace and fourier transform of this function?
| Topic: |
Science > Physics |
| User: |
"Luna Moon" |
| Date: |
20 Aug 2006 05:00:23 PM |
| Object: |
how to compute the laplace and fourier transform of this function? |
Hi there,
Suppose I have a function f(t) which I knew its laplace and fourier
transform.
What is the laplace and fourier transform of the following:
exp(a*f(t))
???
----------------------------
Is there a way to evaluate the laplace transform of
heaviside((exp(x)-a)),
where the heaviside function is also called step function,
heaviside(x) = 1, when x>0, and =0, when x<0, and it has a jump from 0
to 1 at x=0...
---------------------------
Please give me some pointers! thanks a lot!
.
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| User: "Robert Israel" |
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| Title: Re: how to compute the laplace and fourier transform of this function? |
20 Aug 2006 07:38:49 PM |
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In article <1156111223.392350.157580@75g2000cwc.googlegroups.com>,
Luna Moon <lunamoonmoon@gmail.com> wrote:
Hi there,
Suppose I have a function f(t) which I knew its laplace and fourier
transform.
What is the laplace and fourier transform of the following:
exp(a*f(t))
???
No nice formula.
exp(a f(t)) = sum_{n=0}^infty a^n f(t)^n/n!
Now the Fourier transform of a power of f is a "convolution power"
of the Fourier transform of f. But in general that's making matters
more complicated rather than less.
----------------------------
Is there a way to evaluate the laplace transform of
heaviside((exp(x)-a)),
where the heaviside function is also called step function,
heaviside(x) = 1, when x>0, and =0, when x<0, and it has a jump from 0
to 1 at x=0...
Yes, that's easy. Hint: when does exp(x) - a change sign?
Do the cases a <= 0 and a > 0 separately.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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| User: "robert bristow-johnson" |
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| Title: Re: how to compute the laplace and fourier transform of this function? |
21 Aug 2006 10:39:28 PM |
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Luna Moon wrote:
Suppose I have a function f(t) which I knew its laplace and fourier
transform.
What is the laplace and fourier transform of the following:
exp(a*f(t))
???
there is no theorem that will do this nicely. you gotta plug in f(t)
and see what you get.
Is there a way to evaluate the laplace transform of
heaviside((exp(x)-a)),
where the heaviside function is also called step function,
heaviside(x) = 1, when x>0, and =0, when x<0, and it has a jump from 0
to 1 at x=0...
this one can be simplified because of the nature of heaviside(x)
h(x) = heaviside( exp(x) - a ) = heaviside( x - log(a) )
the Laplace transform is
H(s) = Laplace{ h(x) } = 1/s * exp(-s*log(a)) = 1/(s*a^s)
r b-j
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| User: "cnctut" |
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| Title: Re: how to compute the laplace and fourier transform of this function? |
20 Aug 2006 06:44:02 PM |
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Luna Moon wrote:
Hi there,
Suppose I have a function f(t) which I knew its laplace and fourier
transform.
What is the laplace and fourier transform of the following:
exp(a*f(t))
???
----------------------------
Is there a way to evaluate the laplace transform of
heaviside((exp(x)-a)),
where the heaviside function is also called step function,
heaviside(x) = 1, when x>0, and =0, when x<0, and it has a jump from 0
to 1 at x=0...
---------------------------
Please give me some pointers! thanks a lot!
Luna,
Are you trying to find the Laplace of a function f(t)? What is the
function? f(t) = ?
Tut
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| User: "John C. Polasek" |
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| Title: Re: how to compute the laplace and fourier transform of this function? |
21 Aug 2006 07:38:11 PM |
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On 20 Aug 2006 15:00:23 -0700, "Luna Moon" <lunamoonmoon@gmail.com>
wrote:
Hi there,
Suppose I have a function f(t) which I knew its laplace and fourier
transform.
What is the laplace and fourier transform of the following:
exp(a*f(t))
???
----------------------------
Is there a way to evaluate the laplace transform of
heaviside((exp(x)-a)),
where the heaviside function is also called step function,
heaviside(x) = 1, when x>0, and =0, when x<0, and it has a jump from 0
to 1 at x=0...
---------------------------
Please give me some pointers! thanks a lot!
(This message did not appear when I posted it last night)
The Heaviside transform is just like the Laplace except with the
Heaviside, the step function is already built in, as I recall. So the
inverse of the Heaviside is the response to a unit step.
Laplace requires you to specify the input function so the Laplace
transform is s times the Heaviside. See if that doesn't work.
John Polasek
John Polasek
http://www.dualspace.net
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| User: "John C. Polasek" |
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| Title: Re: how to compute the laplace and fourier transform of this function? |
20 Aug 2006 07:39:46 PM |
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On 20 Aug 2006 15:00:23 -0700, "Luna Moon" <lunamoonmoon@gmail.com>
wrote:
Hi there,
Suppose I have a function f(t) which I knew its laplace and fourier
transform.
What is the laplace and fourier transform of the following:
exp(a*f(t))
???
----------------------------
Is there a way to evaluate the laplace transform of
heaviside((exp(x)-a)),
where the heaviside function is also called step function,
heaviside(x) = 1, when x>0, and =0, when x<0, and it has a jump from 0
to 1 at x=0...
---------------------------
Please give me some pointers! thanks a lot!
The Heaviside transform is just like the Laplace except with the
Heaviside, the step function is already built in, as I recall. So the
inverse of the Heaviside is the response to a unit step.
Laplace requires you to specify the input function so the Laplace
transform is s times the Heaviside. See if that doesn't work.
John Polasek
John Polasek
http://www.dualspace.net
.
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