# [SciPy-user] phase wrapping algorithm

Ryan Krauss ryanlists at gmail.com
Tue Oct 10 16:58:13 CDT 2006

```This probably wasn't worth the ammount of time I spent on it, but I'll
submit it to the list in case anyone else is curious or can learn from
it.  This is a bit of a contrived example, but I often find with
experimental data that I have significant noise at high and low
frequncies, so I want to start the phase wrapping in the middle at a
known good point.  So I wrote a phase wrapping algorithm that breaks
the data into two vectors, phase wraps the one above the middle
frequency in the normal way, but needs to step through the one below
the middle frequency in reverse.  The FORTRAN and Python versions are
attached.  phasewrap.py contains the Python implementation and
includes a function to compare the two.  Typical output includes the
attached plot and these times:

FORTRAN time=0.00100302696228
Numpy.unwrap time=0.00893402099609
Numpy/FORTRAN time ratio=8.90705966247
Bryan Cole time=0.00318098068237
Bryan/FORTRAN time ratio=3.17138103161

Bryan's algorithm is exactly the kind of vectorized thinking that I
need to learn how to do.  I think in for loops; I don't know why.

Thanks to everyone who contributed to this,

Ryan

On 10/10/06, Bryan Cole <bryan at cole.uklinux.net> wrote:
> I do this quite a lot in the context of FFTs.
> try:
>
> def unwrap(thetaArray):
>     """takes an array of theta values in degrees
>     returns the data in unwrapped form"""
>     diff = zeros_like(thetaArray)
>     diff[1:] = thetaArray[1:] - thetaArray[:-1]
>     upSteps = diff > 180
>     downSteps = diff < -180
>     shift = cumsum(upSteps) - cumsum(downSteps)
>     return thetaArray - 360*shift
>
> Obviously, a Weave version will be a lot faster, but this is at least
> fully vectorised, so it's not bad.
>
> BC
>
> On Tue, 2006-10-10 at 12:32 -0500, Ryan Krauss wrote:
> > 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?
> >
> > Thanks for your thoughts,
> >
> > 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()
> > _______________________________________________
> > SciPy-user mailing list
> > SciPy-user at scipy.org
> > http://projects.scipy.org/mailman/listinfo/scipy-user
>
>
> _______________________________________________
> SciPy-user mailing list
> SciPy-user at scipy.org
> http://projects.scipy.org/mailman/listinfo/scipy-user
>
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