How do I calculate the amplitude ratio and phase lag for two sinusoidal signals in MATLAB?

How do I calculate the amplitude ratio and phase lag for two sinusoidal signals in MATLAB?

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The amplitude ratio and phase lag for two sinusoidal signals can be determined by taking the Fourier Transform and comparing the magnitude and phase of the signals.

For example:

% clear
clear all
% set the lag
lag = pi/2;
% amplitude for sinusodial 1
amp_x = 2;
% amplitude for sinusodial 2
amp_y = 4;
% Sampling frequency
Fs = 1024;
% Time vector of 0.5 second
t = 0:1/Fs:0.5*(Fs-1)/Fs;
% number of points
npts = length(t);
% Create a sine wave of 20 Hz.
x = amp_x * (sin(2*pi*t*20) + ...
0.25*randn(1,npts)) + 5;
% Create a sine wave of 20 Hz
% with a phase of pi/2.
y = amp_y * (sin(2*pi*t*20 + lag)...
+ 0.25*randn(1,npts));
% remove bias
x = x - mean(x);
y = y - mean(y);
% plot the signal
figure(1)
plot(t,x,t,y);
xlabel('Time (s)');
ylabel('Amplitude');
legend('Signal x(t):sin(2*pi*t*20)',...
'Signal y(t):sin(2*pi*t*20+lag)');
% take the FFT
X=fft(x);
Y=fft(y);

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How do I calculate the amplitude ratio and phase lag for two sinusoidal signals in MATLAB?

How do I calculate the amplitude ratio and phase lag for two sinusoidal signals in MATLAB?