Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

4.3. NONLINEAR PREDICTION OF COMPLEX WAVEFORMS 55
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Figure 4.4: (a) Prediction of Figure 4.2(b) (p = 6). (b) The error between original
data and predicted data.
with additive noise. The prediction for different filter lengths cannot model the
data (p = 3, 5, and 15) in Figures 4.8, 4.9, and 4.10; p = 5 rejects noise but cannot
model the data; p = 15 models the data better than the optimum filter length
but it is also not a perfect solution because it overfits noise in the prediction panel
(Figure 4.10(b)).
Events with nonlinear moveout can be modeled with a Volterra series. I begin
by considering equation (4.8) as a Volterra series expansion by appending nonlinear
coefficients. Remember that although the data vector m in equation (3.25) contains
linear and nonlinear prediction coefficients, the problem is linear in the coefficients.
(b)