angle (MATLAB Function Reference)

Phase angle

P = angle(Z)

Description

P = angle(Z)

returns the phase angles, in radians, for each element of complex array Z. The angles lie between

For complex Z, the magnitude and phase angle are given by

R = abs(Z)        % magnitude
theta = angle(Z)  % phase angle

and the statement

Z = R.*exp(i*theta)

converts back to the original complex Z.

Examples

Z =
1.0000 - 1.0000i   2.0000 + 1.0000i   3.0000 - 1.0000i   4.0000 + 1.0000i
1.0000 + 2.0000i   2.0000 - 2.0000i   3.0000 + 2.0000i   4.0000 - 2.0000i
1.0000 - 3.0000i   2.0000 + 3.0000i   3.0000 - 3.0000i   4.0000 + 3.0000i
1.0000 + 4.0000i   2.0000 - 4.0000i   3.0000 + 4.0000i   4.0000 - 4.0000i

P = angle(Z)
P =

   -0.7854    0.4636   -0.3218    0.2450
    1.1071   -0.7854    0.5880   -0.4636
   -1.2490    0.9828   -0.7854    0.6435
    1.3258   -1.1071    0.9273   -0.7854

Algorithm

angle can be expressed as:

angle(z) = imag(log(z)) = atan2(imag(z),real(z))