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 > > > > >