       Re: Making a phase plot

• To: mathgroup at smc.vnet.net
• Subject: [mg62549] Re: Making a phase plot
• From: John Doty <jpd at whispertel.LoseTheH.net>
• Date: Sun, 27 Nov 2005 02:41:43 -0500 (EST)
• References: <dm95mr\$70i\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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

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