# [SciPy-user] phase wrapping algorithm

Ryan Krauss ryanlists at gmail.com
Tue Oct 10 12:32:24 CDT 2006

```I am rethinking an algorithm for unwrapping phase data from arctan2
for a vector of complex numbers (coming from lti models of feedback
control systems).  I had written something a while ago using weave,
but my old code causes seg faults with a recent scipy update.  So, I
am rethinking the algorithm.

The problem occurs when either because of noise or just the definition
of the inverse tangent, their are discontinuities in the phase (which
is coming from arctan2(imag(vector), real(vector)).  For example, in
the attached plot and data file, there is a point where the phase
passes through -180 degrees.  arctan2 jumps to returning +180, +175
etc, when it makes a pretty plot and makes more sense to me to convert
+175 to -185.  What I had done previously is write a for loop that
compares the current value of the phase to the value at the previous
index (i.e. if phase[i]-phase[-1]>300 or if phase[i]-phase[i-1]<-300)
to find the discontinuities.  Is there a cleaner/faster way to do
this?  (I had done it in weave and will probably now do it in f2py for
comparison on speeds).  I have attached/included a first attempt at an
algorithm that is more vectorized.  But is there a fast, easy way to
compare a vector to the same vector shift one element up or down?
Right now I am doing this

phase2=r_[phase[0:1],phase[0:-1]]

to shift the vector (and reuse the first element so there isn't a jump
from phase[-1] to phase[0] which may legitimately be far apart).

Has anyone else already done this?  Are there obvious bottlenecks with
the algorithm?

Ryan

=====================================
from scipy import arange, io, r_
from pylab import show, figure, subplot, clf, cla, semilogx, xlabel,
ylabel, legend, xlim

import copy

f=data[:,0]
phase=data[:,1]
figure(1)
clf()
startphase=copy.copy(phase)
semilogx(f,startphase)

keepgoing=1

inds=arange(0,len(phase))

while keepgoing:
phase2=r_[phase[0:1],phase[0:-1]]#artificially repeat the first element
diff=phase-phase2
jumps=inds[abs(diff)>250]
keepgoing=jumps.any()
if not keepgoing:
break
ind=jumps.min()
if diff[ind]>0:
phase[ind:]-=360
else:
phase[ind:]+=360

semilogx(f,phase,'r--')

legend(['Before unwrapping','after unwrapping'],2)

xlim([1,30])

show()
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