Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

4.5. SYNTHETIC AND REAL DATA EXAMPLES 66
Time (s)
0
0.2
0.4
0.6
Traces
10 20
Time (s)
0.6
(a) (b)
Time (s)
0
0.2
0.4
0
0.2
0.4
0.6
Traces
10 20
Traces
10 20
Time (s)
Time (s)
0
0.2
0.4
0.6
Traces
10 20
(c)
0.6
(e) (d) (f) (e)
0
0.2
0.4
Traces
10 20
Figure 4.13: 2-D synthetic data for comparison of prediction between linear prediction
theory and the cubic part of a Volterra series. (a) Original data. (b) Prediction
using linear prediction theory with parameter p = 3. (c) Error between original data
and predicted data via linear prediction theory. (d) Prediction using the cubic part
of a Volterra series with parameter r = 3. (e) Error between original data and
predicted data via the cubic part of a Volterra series.
with parameter p = 6, respectively. The prediction is good and the data are properly
modeled but there is a small amount of coherent energy in the noise panel (Figure
4.15(c)). The prediction of the linear prediction method is very poor, the signals
are leaking into the error panel (Figure 4.15(e)).