Shift phase angles
Q = unwrap( unwraps the radian phase angles
in a vector
P. Whenever the jump between consecutive angles is greater
than or equal to π radians,
unwrap shifts the angles
by adding multiples of ±2π until the jump is less than
P is a matrix,
operates columnwise. If
P is a multidimensional array,
unwrap operates on the first dimension whose size is larger than
Define the - and -coordinates of a spiral with phase angle from 0 to . Plot the spiral.
t = linspace(0,6*pi,201); x = t/pi.*cos(t); y = t/pi.*sin(t); plot(x,y)
Find the phase angle of the spiral from the - and -coordinates using the
atan2 function. The
atan2 function returns the angle values within the closed interval from to .
P = atan2(y,x); plot(t,P)
Note that this plot has discontinuities. Use
unwrap to eliminate the discontinuities.
unwrap adds multiples of when the phase difference between consecutive elements of
P are greater than or equal to the jump threshold radians. The shifted phase angle
Q lies in the interval from 0 to .
Q = unwrap(P); plot(t,Q)
Shift the phase angle of a frequency response. The phase curve has two jumps. The first jump is
3.4250 radians between
W = 3 and
W = 3.4, and the second jump is
6.3420 radians between
W = 5 and
W = 5.4. Plot the phase curve.
clear; close all; W = [0:0.4:3, 3.4:0.4:5, 5.4:0.4:7]; P = [-1.5723 -1.5747 -1.5790 -1.5852 -1.5922 -1.6044 -1.6269 -1.6998 1.7252 1.5989 1.5916 1.5708 1.5582 -4.7838 -4.8143 -4.8456 -4.8764 -4.9002]; plot(W,P,'bo-')
unwrap to shift the phase angle using the default jump threshold radians. Plot the shifted phase curve. Both jumps are shifted since they are greater than the jump threshold radians.
Now shift the phase angle using a jump threshold of
5 radians. Plot the shifted phase curve. The first jump is not shifted since it is less than the jump threshold
Define a two-column matrix
P that contains phase angles.
P = [0 7.07; 0.19 0.98; 6.67 1.18; 0.59 1.37; 0.78 1.56]
P = 5×2 0 7.0700 0.1900 0.9800 6.6700 1.1800 0.5900 1.3700 0.7800 1.5600
The phase angles
P(1,2) = 7.07 and
P(3,1) = 6.67 have phase differences that are larger than compared to the rest of the data.
Unwrap the phase angles by first comparing the elements columnwise. Specify the
dim argument as 1. Use the default jump threshold by specifying the second argument as
dim = 1; P1 = unwrap(P,,dim)
P1 = 5×2 0 7.0700 0.1900 7.2632 0.3868 7.4632 0.5900 7.6532 0.7800 7.8432
To shift phase angles by rows instead of by columns, specify
dim as 2 instead of 1.
dim = 2; P2 = unwrap(P1,,dim)
P2 = 5×2 0 0.7868 0.1900 0.9800 0.3868 1.1800 0.5900 1.3700 0.7800 1.5600
P— Input array
Input array, specified as a vector, matrix, or multidimensional array.
tol— Jump threshold to apply phase shift
pi(default) | scalar
Jump threshold to apply phase shift, specified as a scalar. A jump threshold less than π has the same effect as the default threshold π.
dim— Dimension to operate along
Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.
unwrap(P,,1) operates along the columns of
P and returns the shifted phase angle of each column.
unwrap(P,,2) operates along the rows of
P and returns the shifted phase angle of each row.
dim is greater than
Q— Shifted phase angle
Shifted phase angle, returned as a vector, matrix, or multidimensional array. The
size of the output
Q is always the same as the size of the input
Usage notes and limitations:
Row vector input is only supported when the first two inputs are vectors and nonscalar.
Performs arithmetic in the output class. Therefore, results might not match MATLAB® due to different rounding errors.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).