Model fitting by least squares

From the frequency domain to the time domain

Equation (2.4) is a frequency-domain quadratic form that we minimized by varying a single parameter, a Fourier coefficient. Now we will look at the same problem in the time domain. We will see that the time domain offers flexibility with boundary conditions, constraints, and weighting functions. The notation will be that a filter $f_t$ has input $x_t$ and output $y_t$. In Fourier space this is $Y=XF$. There are two problems to look at, unknown filter $F$ and unknown input $X$.