angle (Signal Processing Toolbox)

Phase angle.

Syntax

p = angle(h)

Description

p = angle(h)

returns the phase angles, in radians, of the elements of complex vector or array h. The phase angles lie between -

and

For complex sequence h = x + iy = me^ip, the magnitude and phase are given by

m = abs(h)
p = angle(h)

To convert to the original h from its magnitude and phase:

i = sqrt(-1)
h = m.*exp(i*p)

The angle function is part of the standard MATLAB language.

Example

Calculate the phase of the FFT of a sequence:

t = (0:99)/100;                      % time vector
x = sin(2*pi*15*t) + sin(2*pi*40*t); % signal
y = fft(x);                          % compute DFT of x
p = unwrap(angle(y));                % phase

Plot the phase:

f = (0:length(y)-1)'/length(y)*100;  % frequency vector
plot(f,p)

Algorithm

angle can be expressed as:

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