Re: Strange behaviour of Fourier[] in Mathematica 7

• To: mathgroup at smc.vnet.net
• Subject: [mg93974] Re: Strange behaviour of Fourier[] in Mathematica 7
• From: WetBlanket <Wyvern864 at gmail.com>
• Date: Sun, 30 Nov 2008 06:59:39 -0500 (EST)
• References: <ggr257\$e5r\$1@smc.vnet.net>

```On Nov 29, 3:31 am, "Guy Lamouche" <noem... at noemail.com> wrote:
> I came across the following strange behaviour in Mathematica 7 on my syst=
em.
>
> Here is some data generated in an intermediate calculation:
>
> data = {-0.00023798861821554878` + 0.` I,
>   0.0006139487084761968` -
>    0.001435108611558083` I, -0.001710424871758314` +
>    0.0069296921181465935` I,
>   0.0019942263545704086` - 0.021565769535630507` I,
>   0.002517554651534451` +
>    0.04381651818448262` I, -0.01220847735732839` -
>    0.05813547502399065` I,
>   0.018746602690952168` +
>    0.050324001393803136` I, -0.01572173179907872` -
>    0.028359695723765642` I,
>   0.007974058406218107` +
>    0.010364643233016675` I, -0.0025342667815659334` -
>    0.0024424248976939247` I, 0.`, 0.`, 0.`, 0.`, 0.`, 0.`, 0.`, 0.`,
>   0.`, 0.`, 0.`}
>
> If I compute the discrete Fourier transform by applying directly the form=
ula
> used by Mathematica (as described in the documentation for Fourier), I ge=
t a
> nice transform with real and imaginary parts (the following is not intend=
ed
> to be read, but pasted in Mathematica front-end):
>
> n = Length[data];
> u[s_] = 1/Sqrt[n] \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(r =
>       1\), \(n\)]\(data[\([\)\(r\)\(]\)]\ Exp[
>       I\ 2.  \[Pi] \((r - 1)\) \((s - 1)\)/n]\)\);
> dataTF1 = Table[u[i], {i, 1, n}];
> ListPlot[{dataTF1 // Re, dataTF1 // Im}, PlotRange -> All,
>  PlotStyle -> {Blue, Red}]
>
> If I use Fourier[], the imaginary part is put to zero!!!
>
> dataTF2 = Fourier[data];
> ListPlot[{dataTF2 // Re, dataTF2 // Im}, PlotRange -> All,
>  PlotStyle -> {Blue, Red}]
>
> This behaviour occurs on my system only for some data like the one above,
> but it does occur. There is no problem with 6.0.3 on another computer sin=
ce
> the result is the same for both calculations above.
>
> I would like to know if this happens also on other's computer with
> Mathematica 7? I am using the windows version ("7.0 for Microsoft Windows
> (32-bit) (November 10, 2008)") under Vista Business SP1.
>
>
> Guy Lamouche

I am running V7 on a Dell Laptop (XPS M2010) under Windows XPS and I
get the same results with both methods.  I copied the code directly