# Re: Want a smooth function from Arg[ ]

```Hi Ryan,
try this:

data1 = Arg[data];
data2 = FoldList[Round[(#1-#2)/(2Pi)] 2Pi+
#2&,First[data1],Rest[data1]]; ListPlot[data2]

Jrgen

-----Original Message-----
mathgroup@smc.vnet.net
Subject: [mg12251] [mg12213] Want a smooth function from Arg[ ]

>
>I need to be able to fit an nth degree polynomial to the phase function
>for  a list of data.  However, the Arg[x] function wraps the phase at
>+/- Pi  creating discontinuities in what would be a smooth function.
>To clearify, let me give the following example:
>
>Create a list of data with a  gaussian profile and quadratic phase:
>
>nn=128;
>a=0.005; b=0.003;
>data=Table[N[Exp[-a*(t-nn/2)^2+I*b*(t-nn/2)^2]], {t,nn}];
>
>Plot the magnitude and phase:
>
>ListPlot[Abs[data],PlotRange->{0,1},PlotJoined->True,
>  PlotLabel->FontForm[
>      "Absolute value of waveform",{"Helvetica-Bold",10}]]
>ListPlot[Arg[data], PlotJoined->True, PlotRange->All,
>   PlotLabel->FontForm[ "Phase of time waveform",
>{"Helvetica-Bold",10}]]
>
>I would like to now fit a curve to this phase (which should be 0.003*x^2
>).
> However, the wrapping of the phase would seem to make this difficult to
>do  directly.  Any ideas on how to manipulate the results of Arg to
>give a  continuous function of data?
>
>Thanks,
>
>Ryan
>
>--
>________________________________________________
>
>  Ryan P. Scott
>  Laser and Electro-Optics Research Group
>  UC Davis - Department of Applied Science
>  Tel: (530)754-4358  Fax: (530)752-1652
>  Email: scott@leorg.ucdavis.edu
>________________________________________________
>
>

```

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