# Retrieve phase from a time-varying cosine signal

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Jingtao on 27 May 2023
Commented: Jingtao on 28 May 2023
I got two experimental time-domain signals (sampling length of N=13001, sampling frequency of Fs=4000 Hz). By curve fitting, I found one (red) is a cosine signal with a single frequency, so the phase shift is linear with respect to time. However, the other (blue) is a time-varying cosine singal whose phase shift is nonliear with respect to time. How can I get the phase difference between the red signal and the blue one? Please find attached "data.txt".

Hiro Yoshino on 27 May 2023
I would suggest that you should try hilbert transform as follows:
plot(data(:,1))
hold on
plot(data(:,2));
hold off;
Hilbert transform and phase analysis
y1 = hilbert(data(:,1));
y2 = hilbert(data(:,2));
phase1 = atan2(imag(y1),real(y1));
phase2 = atan2(imag(y2),real(y2));
plot(unwrap(phase1)); % unwrap phases
hold on;
plot(unwrap(phase2));
hold off;
plot(unwrap(phase1) - unwrap(phase2));
title("Phase difference");
Jingtao on 28 May 2023
Hi Hiro, Thanks a lot. Nice!