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MathGroup Archive 2004

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Re: Problem with function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48316] Re: Problem with function
  • From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
  • Date: Mon, 24 May 2004 00:45:10 -0400 (EDT)
  • References: <c8ptmu$kne$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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
>
>


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