Can any Fourier series be interpreted as a (non-)linear regression model

2018-03-12 20:23:42

I was asked to answer the following question: "Can any Fourier series be interpreted as a (non-)linear regression model? If not, what are the limitations of Fourier analysis?" I thought this was true, but my lecturer says it is not. Can someone explain me why? I thought that you can always write a Fourier series as

$$Y_i=\beta_0+\beta_1\sin\left(\frac{2\pi}{T} t\right)+\beta_2\cos\left(\frac{2\pi}{T} t\right)+\beta_3\sin\left(\frac{4\pi}{T} t\right)+\beta_4\cos\left(\frac{4\pi}{T} t\right)+...+\\\beta_{2N}\cos\left(\frac{2\pi N}{T} t\right)$$

which is a linear regression model.