identifying phase shift between signals

Question

I have generated three identical waves with a phase shift in each. For example:

t = 1:10800; % generate time vector
fs = 1; % sampling frequency (seconds)
A          


        

Answer 1

Here is the little modification of your code: phi = 10 is actually in degree, then in sine function, phase information is mostly expressed in radian,so you need to change deg2rad(phi) as following:

t = 1:10800; % generate time vector
fs = 1; % sampling frequency (seconds)
A = 2; % amplitude
P = 1000; % period (seconds), the time it takes for the signal to repeat itself
f1 = 1/P; % number of cycles per second (i.e. how often the signal repeats itself every second).
y1 = A*sin(2*pi*f1*t); % signal 1
phi = deg2rad(10); % phase shift 
y2 = A*sin(2*pi*f1*t + phi); % signal 2
phi = deg2rad(15); % phase shift
y3 = A*sin(2*pi*f1*t + phi); % signal 3

YY = [y1',y2',y3'];

plot(t,YY)

then using frequency domain method as mentioned chipaudette

fft_y1 = fft(y1);
fft_y2 = fft(y2);
phase_rad = angle(fft_y1(1:end/2)/fft_y2(1:end/2));
phase_deg = rad2deg(angle(fft_y1(1:end/2)/fft_y2(1:end/2)));

now this will give you a phase shift estimate with error = +-0.2145