%% Phase Response
% MATLAB® functions are available to extract the phase response of a filter. Given a frequency response, the function abs returns the magnitude and angle returns the phase angle in radians. To view the magnitude and phase of a Butterworth filter using fvtool:

d = designfilt('lowpassiir','FilterOrder',9, ...
    'HalfPowerFrequency',400,'SampleRate',2000);
fvtool(d,'Analysis','freq')

% You can also click the Magnitude and Phase Response button on the toolbar or select Analysis > Magnitude and Phase Response to display the plot.
%
% The unwrap function is also useful in frequency analysis. unwrap unwraps the phase to make it continuous across 360° phase discontinuities by adding multiples of ±360°, as needed. To see how unwrap is useful, design a 25th-order lowpass FIR filter:

h = fir1(25,0.4);

%
% Obtain the frequency response with freqz and plot the phase in degrees:

[H,f] = freqz(h,1,512,2);
plot(f,angle(H)*180/pi)
grid

%
% It is difficult to distinguish the 360° jumps (an artifact of the arctangent function inside angle) from the 180° jumps that signify zeros in the frequency response.
% unwrap eliminates the 360° jumps:

plot(f,unwrap(angle(H))*180/pi)

%
% Alternatively, you can use phasez to see the unwrapped phase:

phasez(h,1)

% Copyright 2012 The MathWorks, Inc.