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Want a smooth function from Arg[ ]

• To: mathgroup@smc.vnet.net
• Subject: [mg12213] Want a smooth function from Arg[ ]
• From: scott@vader.engr.ucdavis.edu (Ryan Scott)
• Date: Fri, 1 May 1998 03:09:00 -0400
• Organization: UC Davis - Dept. Applied Science

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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  • Re: Want a smooth function from Arg[ ]
    • From: Daniel Lichtblau <danl@wolfram.com>