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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')

Figure Filter Visualization Tool - Magnitude Response (dB) and Phase Response contains an axes object and other objects of type uitoolbar, uimenu. The axes object with title Magnitude Response (dB) and Phase Response contains an object of type line.

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

Figure contains an axes object. The axes object contains an object of type line.

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)

Figure contains an axes object. The axes object contains an object of type line.

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

phasez(h,1)

Figure contains an axes object. The axes object with title Phase Response contains an object of type line.

See Also

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