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: an=2/n * sum ( x(t) cos (2*pi*k*t/n)); bn=2/n * sum ( x(t) sin (2*pi*k*t/n))
but I can't get values which Matlab showed me for these coefficients.
Is that Matlab formula for Fourier model formula for trigonometric Fourier series? Because in literature the first term in formula is a0/2, here is a0?
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: an=2/n * sum ( x(t) cos (2*pi*k*t/n)); bn=2/n * sum ( x(t) sin (2*pi*k*t/n))
but I can't get values which Matlab showed me for these coefficients.
Is that Matlab formula for Fourier model formula for trigonometric Fourier series? Because in literature the first term in formula is a0/2, here is a0?
