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A more Matlab compatible version of unwrap.m
From: |
lash |
Subject: |
A more Matlab compatible version of unwrap.m |
Date: |
Sat, 17 Oct 1998 18:31:12 -0500 (CDT) |
Thanks to Larry and John who explained how the Matlab version of
unwrap works, and Francesco for suggesting that cumsum() would
probably be more efficient (and easier to understand) than
filter, I have changed the unwrap function that I wrote to be
more Matlab compatible.
I think I have verified that it works as expected, but if you
find a problem, let me know.
Bill Lash
address@hidden
## Usage: b = unwrap(a{,tol{,dim}})
##
## Unwrap radian phases by detecting jumps greater in magnitude
## than "tol" (default pi) and adding or subtracting 2*pi as
## appropriate.
##
## Unwrap will unwrap along the columns of "a" unless the row
## dimension of "a" is 1 or the "dim" argument is given with a
## value of 1, when it will unwrap along the row(s).
## Verification steps:
##
## r = [0:100]; #original vector
## w = r - 2*pi*floor((r+pi)/(2*pi)); #wrapped version value between
-pi and pi
##
## max(abs(r-unwrap(w))) #unwrap single row
## max(abs(r'-unwrap(w'))) #unwrap single column
## max(max(abs([r',r']-unwrap([w',w'])))) #unwrap 2 columns
## max(max(abs([r;r]-unwrap([w;w],[],1)))) #unwrap 2 rows by specifying
dimension
## max(abs((r+10)-unwrap(10+w))) #verify that first element
greater than pi will
## #not cause problems
##
## max(abs(w'-unwrap(w',[],1))) #unwrapping a col vector by
rows should not change it
## max(abs(w-unwrap(w,[],2))) #unwrapping a row vector by
cols should not change it
## max(max(abs([w;w]-unwrap([w;w])))) #unwrapping 2 rows by cols
should not change
##
## max(abs(r-unwrap(w,0.8))) #verify that setting tolerance
too low will cause
## #different (bad) results.
## Bill Lash
## address@hidden
function retval = unwrap(a,tol,dim)
if ((nargin<1) || (nargin>3))
usage("unwrap(a,[tol,[dim]])")
endif
if (nargin < 3)
if (rows(a)==1)
dim = 1; #row vector, go along the row
else
dim = 2; # Otherwise go along the columns
endif
endif
if (nargin < 2)
tol = pi;
endif
if (tol == []) # if tol is not provided but dim is, handle it
tol = pi;
endif
tol = abs(tol); # don't let anyone use a negative tol
rng = 2*pi;
#
# Want to get data in a form so that we can unwrap each column
#
if (dim == 1)
ra = a.';
else
ra = a;
endif
n = columns(ra);
m = rows(ra);
if (m == 1) # Handle case where we are trying to unwrap
retval = a; # a scalar, or only have one sample in the
return; # specified dimension
endif
#
# take first order difference to see so that wraps will show up
# as large values, and the sign will show direction
#
d = [zeros(1,n);ra(1:m-1,:)-ra(2:m,:)];
#
# Find only the peaks, and multiply them by the range so that there
# are kronecker deltas at each wrap point multiplied by the range
# value
#
p = rng * (((d > tol)>0) - ((d < -tol)>0));
#
# Now need to "integrate" this so that the deltas become steps
#
r = cumsum(p);
#
# Now add the "steps" to the original data and put output in the
# same shape as originally
#
if (dim == 1)
retval = (ra + r).';
else
retval = (ra + r);
endif
endfunction
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