How does phasez work?

Question

Nathan Jessurun 2018-12-10

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https://ww2.mathworks.cn/matlabcentral/answers/435035-how-does-phasez-work

回答： Miriam Guadalupe Cruz Jimenez 2019-8-13

I thought phasez simply plots the unwrapped version of a filter's angle. However, I get different plots for the following methods:

% Filter to add reverb to sample -- Requires DSP toolbox
% Use the impulse response from a reverb-y building as the time domain filter impulse repsonse
[timeFilter, Fs] = audioread('ChurchImpulseResponse-16-44p1-mono-5secs.wav');
% For an FIR filter, the time domain coefficients are the taps of the filter
h = freqz(timeFilter, [1 zeros(1, length(timeFilter))]);
[phi, w] = phasez(h);
plot(w, phi);
hold on;
plot(w, unwrap(angle(h)));
xlabel('frequency (rad/sample)');
ylabel('phase (radians)')
legend({'phasez', 'unwrap(angle)'});

What causes these two plots to behave quite differently for the produced filter? Note that for most filters I've tried, these plot operations are synonymous.

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Answer 1

Miriam Guadalupe Cruz Jimenez 2019-8-13

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Hi! Indeed 'phasez()' plots the unwrapped angle, but 'phasez()' acts on the coefficients of the filter and 'unwrap(angle())' acts on the frequency response of the filter. Thus, in your code you should employ 'timeFilter' as the argument in 'phasez()' and 'h' as the argument of 'unwrap(angle())'. Attached your sample code with this modification.

timeFilter = [1 2 3 4 5 6 7 8 9];
h = freqz(timeFilter, [1 zeros(1, length(timeFilter))]);
[phi, w] = phasez(timeFilter);
plot(w, phi);
hold on;
plot(w, unwrap(angle(h)),'o');
xlabel('frequency (rad/sample)');
ylabel('phase (radians)')
legend({'phasez', 'unwrap(angle)'});