Estimating the prediction filter coefficients

For sake of simplicity, we denote $W_{\rm j}=W(f,j\Delta x)$. $W_{\rm j}$ is predictable from $W_{\rm j-1}, W_{\rm j-2},..., W_{\rm j-N}$.  

$$W_{\rm j}=\sum_{\rm z=1}^{\rm N}C_{\rm z}W_{\rm j-z}$$ (29)

Actually, equation (29) is a convolution operator. For each frequency f, we have an equation like (29). All frequencies have the same prediction filter $C_1, C_2,..., C_{\rm N}$. Usually this is an over-determined system. We can use some optimization method to solve it, e.g., conjugate gradient, LSQR, Lanzcos, etc.