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.

# Question about fourier transform and laplace transform

Started by ●February 1, 2008

Reply by ●February 1, 20082008-02-01

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 differencebetween>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 weare>using Fourier transform. Can we get >Fourier transform by replacing s by jw in a Laplace transform? >pls make me clear any one. > > >

Reply by ●February 1, 20082008-02-01

"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

Reply by ●February 1, 20082008-02-01

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

Reply by ●February 1, 20082008-02-01

On Feb 2, 3:33 pm, robert bristow-johnson <r...@audioimagination.com> wrote:> 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-jI have yet to measure a time signal that started before I switched it on!!

Reply by ●February 2, 20082008-02-02

sheepshaggerx@yahoo.co.uk wrote:> On Feb 2, 3:33 pm, robert bristow-johnson <r...@audioimagination.com> > wrote: >> 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 > > 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. �����������������������������������������������������������������������