How to find annual amplitude and phase of time series
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There are a number of ways you can try and estimate it. Do you have a priori knowledge of the frequency? If so you can use linear regression to find the amplitude and phase.
For example, assume I know the frequency is 10 Hz for data sampled at 100 Hz.
Fs = 100; t = 0:1/Fs:2-1/Fs; x = 1.5*cos(2*pi*10*t-pi/4)+randn(size(t)); % create the design matrix X = ones(length(x),3); X(:,2) = sin(2*pi*10*t); X(:,3) = cos(2*pi*10*t); x = x(:); beta = X\x;
The amplitude estimate is:
amp_est = norm([beta(2) beta(3)],2)
The phase angle estimate is:
phase_est = atan2(-beta(2),beta(3))
If you don't know the frequency a priori, then look at the following example: