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MathGroup Archive 2005

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Re: Fourier Transfer and a game?!?!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54233] Re: Fourier Transfer and a game?!?!
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 14 Feb 2005 00:57:49 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <cuf5kg$god$1@smc.vnet.net> <cukb23$lmi$1@smc.vnet.net> <cump6f$3t9$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <cump6f$3t9$1 at smc.vnet.net>, Maxim <ab_def at prontomail.com> 
wrote:

> Here's how we can apply Fourier to this problem:
> 
> In[2]:=
> F = Fourier;
> IF = InverseFourier;
> SetOptions[#, FourierParameters -> {1, 1}]& /@ {F, IF};
> 
> Module[{L},
>    L = PadRight[{0., .35, .35, .15, .15}, 13];
>    IF[.4*F[L]^0 + .35*F[L]^1 + .15*F[L]^2 + .1*F[L]^3] // Chop
> ]

Two comments:

[1] SetOptions accepts a list of functions:

  SetOptions[{Fourier, InverseFourier}, FourierParameters -> {1, 1}]

[2] One can use the Dot product as follows:

  InverseFourier[{0.4, 0.35, 0.15, 0.1} . 
    (Fourier[PadRight[{0., 0.35, 0.35, 0.15, 0.15}, 13]]^# & /@ 
      {0, 1, 2, 3})]

There can be a problem with 0^0 using either approach.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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