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MathGroup Archive 2005

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Re: Making a phase plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62559] Re: Making a phase plot
  • From: Peter Pein <petsie at dordos.net>
  • Date: Mon, 28 Nov 2005 00:57:40 -0500 (EST)
  • References: <dm95mr$70i$1@smc.vnet.net> <dmbr0d$qhs$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

John Doty schrieb:
> Milind Gupta wrote:
> 
>> Hello,
>>      I wanted to plot the phase of a transfer function. I was doing it like
>> this:
>>
>> LogLinearPlot[Phase[w], {w, 0, wmax}]
>>
>>     Where Phase is calculated using the ArcTan function. The problem is tha=
>> t
>> the ArcTan function rounds up the result to positive values when the phase
>> goes below -pi. But I want the phase to keep going negative values upto
>> infinity. Is there a way to do this using some standard functions?
> 
> Well, of course ArcTan can't tell which branch you want. If you can make 
> a list of your phases, sampled often enough that the phase difference is 
> always less than Pi, the following will unwind them, figuring out which 
> branch to use:
> 
> unwind[ p_ ] := Module [
> 	{
> 		off = 0,
> 		pi = Pi//N,
> 		r = p,
> 		t,
> 		i
> 	},
> 	
> 	For[ i = 2, i <= Length[ p ], i += 1,
> 		r[[i]] += off;
> 		If[ Abs[ r[[i]]-r[[i-1]]] > pi,
> 			t = 2 pi Sign[ r[[i]]-r[[i-1]]];
> 			off -= t;
> 			r[[i]] -= t
> 		]
> 	];
> 	r
> ]
> 
> Wrote this about 10 years ago for a demodulator design project. I think 
> it's about the longest and most procedural Mathematica function I ever 
> wrote. Not my usual style at all, but it worked...
> 
> -jpd
> 
Hi John,

it is quite easy to do this in a more functional way (calling your 
function "oldunwind"):

In[1]:= oldUnwind[p_] := (* see above *)
In[2]:= unwind[p_] := p +
   2*Pi*(Flatten[MapIndexed[Table[#2, {Length[#1]}] & ,
     Split[p, Abs[#1 - #2] < Pi & ]]] - 1);
In[3]:= tb = N[Table[Mod[i*Pi, 2*Pi, -Pi], {i, -3, 3, 2/3}]]
Out[3]=
  {-3.141592653589793, -1.0471975511965976, 1.0471975511965976,
   -3.141592653589793, -1.0471975511965976, 1.0471975511965976,
   -3.141592653589793, -1.0471975511965976, 1.0471975511965976,
   -3.141592653589793}
In[4]:= unwind[tb]
Out[4]=
{-3.141592653589793, -1.0471975511965976, 1.0471975511965976,
   3.141592653589793, 5.235987755982989, 7.330382858376184,
   9.42477796076938, 11.519173063162574, 13.61356816555577,
   15.707963267948966}
In[5]:= % === oldUnwind[tb]
Out[5]= True

Regards,
   Peter


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