I am using cftool in Matlab to fit time series values to Fourier model with 8 terms:
General model Fourier8: f(x) = a0 + a1*cos(x*w) + b1*sin(x*w) + a2*cos(2*x*w) + b2*sin(2*x*w) + a3*cos(3*x*w) + b3*sin(3*x*w) + a4*cos(4*x*w) + b4*sin(4*x*w) + a5*cos(5*x*w) + b5*sin(5*x*w) + a6*cos(6*x*w) + b6*sin(6*x*w) + a7*cos(7*x*w) + b7*sin(7*x*w) + a8*cos(8*x*w) + b8*sin(8*x*w)
But I don't understand how Matlab calculate a and b coefficients. I found in literature that I can use formulas:
ak=2/n * sum ( x(t) cos (2*pikt/n))
bk=2/n * sum ( x(t) sin (2*pikt/n)) where n is number of terms in time series, k is index of current term k=1,...n, sum is with t,
but I can't get values which Matlab showed me for these coefficients.
Is Matlab General model Fourier8- formula for trigonometric Fourier series? Because in literature the first term in formula is a0/2, here is a0? Also Matlab value for a0 is not mean value. How to calculate this correct?