# Question about fourier transform and laplace transform

Started by February 1, 2008
```Hi
I am a computer engineering student.I have to know the difference between
Fourier transform and Laplace transform. Because we have studied laplace
transform previous semester, that time to find a frequency response of a
system we replaced s by jw in a s domain transfer function, but now we are
using Fourier transform. Can we get
Fourier transform by replacing s by jw in a Laplace transform?
pls make me clear any one.

```
```Hi,

There was a discussion on this topic earlier.

http://www.dsprelated.com/showmessage/89022/1.php

Regards
Bharat

www.arithos.com

>I am a computer engineering student.I have to know the difference
between
>Fourier transform and Laplace transform. Because we have studied laplace
>transform previous semester, that time to find a frequency response of a
>system we replaced s by jw in a s domain transfer function, but now we
are
>using Fourier transform. Can we get
>Fourier transform by replacing s by jw in a Laplace transform?
>pls make me clear any one.
>
>
>
```
```"Can we get Fourier transform by replacing s by jw in a Laplace
transform?"

The simple answer to this is "yes".  Here is some reference material on
the relationship between the Fourier and Laplace transforms.

http://www.dspguide.com/ch32.htm

Download the pdf file-- the material is not yet available in html
Regards,
Steve
```
```On Feb 1, 8:07 am, "nadunalexander" <nadunalexan...@yahoo.com> wrote:
>
> Can we get Fourier transform by replacing s by jw in a Laplace transform?

the *double-sided* Laplace transform becomes the Fourier Transform
when jw is subsitituted for s.  most of the time in engineering
textbooks, the Laplace Transform is expressed as a single-sided
integral (from 0 to +inf) and when you use the L.T. to solve a system
of linear differential equations, there is an elegant way to include
initial conditions in the single-sided L.T.  the single-sided L.T. is
equivalent to the double-sided L.T of a function that has an implicit
unit step (that begins at a non-negative "t0") multiplying it and most
of the tables of L.T. pairs make that assumption.  in that case,
substituting "jw" in for "s" will get you the F.T., but only for time
functions that are zero for all negative t.

r b-j

```
```On Feb 2, 3:33 pm, robert bristow-johnson <r...@audioimagination.com>
wrote:
>
>
>
> > Can we get Fourier transform by replacing s by jw in a Laplace transform?
>
> the *double-sided* Laplace transform becomes the Fourier Transform
> when jw is subsitituted for s.  most of the time in engineering
> textbooks, the Laplace Transform is expressed as a single-sided
> integral (from 0 to +inf) and when you use the L.T. to solve a system
> of linear differential equations, there is an elegant way to include
> initial conditions in the single-sided L.T.  the single-sided L.T. is
> equivalent to the double-sided L.T of a function that has an implicit
> unit step (that begins at a non-negative "t0") multiplying it and most
> of the tables of L.T. pairs make that assumption.  in that case,
> substituting "jw" in for "s" will get you the F.T., but only for time
> functions that are zero for all negative t.
>
> r b-j

I have yet to measure a time signal that started before I switched it
on!!
```
```sheepshaggerx@yahoo.co.uk wrote:
> On Feb 2, 3:33 pm, robert bristow-johnson <r...@audioimagination.com>
> wrote:
>>
>>
>>
>>> Can we get Fourier transform by replacing s by jw in a Laplace transform?
>> the *double-sided* Laplace transform becomes the Fourier Transform
>> when jw is subsitituted for s.  most of the time in engineering
>> textbooks, the Laplace Transform is expressed as a single-sided
>> integral (from 0 to +inf) and when you use the L.T. to solve a system
>> of linear differential equations, there is an elegant way to include
>> initial conditions in the single-sided L.T.  the single-sided L.T. is
>> equivalent to the double-sided L.T of a function that has an implicit
>> unit step (that begins at a non-negative "t0") multiplying it and most
>> of the tables of L.T. pairs make that assumption.  in that case,
>> substituting "jw" in for "s" will get you the F.T., but only for time
>> functions that are zero for all negative t.
>>
>> r b-j
>
> I have yet to measure a time signal that started before I switched it
> on!!

So?

Jerry
--
Engineering is the art of making what you want from things you can get.
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```