Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Problem with function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48354] Re: Problem with function
  • From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
  • Date: Tue, 25 May 2004 07:17:25 -0400 (EDT)
  • References: <c8ptmu$kne$1@smc.vnet.net> <c8rulh$8m6$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

....and to make the result the same as the one Bob Hanlon provided you make
the replacement

Derivative[1][DiracDelta][\[Omega]]  -> 0

in the result I gave before.

This is allowed because, although the derivative of a Dirac delata function
is a positive impulse immediately followed by a negative impulse, the effect
of these impulses cancels when they are used to weight the integrand in in
any sufficiently smooth integral

Steve Luttrell
West Malvern, UK

"Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk> wrote in
message news:c8rulh$8m6$1 at smc.vnet.net...
> Define your function.
>
> f[t_] := (UnitStep[t] - UnitStep[t - 1])*t +
> (UnitStep[t - 1] - UnitStep[t - 3])*(3/2 - t/2)
>
> Fourier transform your function.
>
> Expand[FourierTransform[f[t], t, \[Omega]]]
>
> which gives
>
>
> -(1/(Sqrt[2*Pi]*\[Omega]^2)) + (3*E^(I*\[Omega]))/
> (2*Sqrt[2*Pi]*\[Omega]^2) - E^(3*I*\[Omega])/
> (2*Sqrt[2*Pi]*\[Omega]^2) - I*Sqrt[Pi/2]*
> Derivative[1][DiracDelta][\[Omega]] +
> (3/2)*I*E^(I*\[Omega])*Sqrt[Pi/2]*
> Derivative[1][DiracDelta][\[Omega]] -
> (1/2)*I*E^(3*I*\[Omega])*Sqrt[Pi/2]*
> Derivative[1][DiracDelta][\[Omega]]
>
> Steve Luttrell
>
> "DJkapi" <djkapi at poczta.onet.pl> wrote in message
> news:c8ptmu$kne$1 at smc.vnet.net...
> > How to compute in Mathematica  fourier transform  of function:
> >
> >             t     ,0=< t =<1
> > g(t)=
> >             1.5-0.5t , 1< t =<3
> >
> > to tell the truth i dont even know how to make Mathematica print that
> > function.
> >
> > Regards,
> > DJKapi
> >
> >
>


  • Prev by Date: Making new Contexts in Modules in a package
  • Next by Date: RE: Min[], Max[]
  • Previous by thread: Re: Problem with function
  • Next by thread: Re: Problem with function