Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser
Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser
Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser
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4.4 (a) <strong>Prediction</strong> <strong>of</strong> Figure 4.2(b) (p = 6). (b) The error between origi-<br />
nal data and predicted data. . . . . . . . . . . . . . . . . . . . . . . 55<br />
4.5 (a) <strong>Prediction</strong> <strong>of</strong> Figure 4.2(b) (p = 15). (b) The error between<br />
original data and predicted data. . . . . . . . . . . . . . . . . . . . 56<br />
4.6 Synthetic data example for different filter lengths. . . . . . . . . . 57<br />
4.7 Optimality <strong>of</strong> filter length for the data in Figure 4.6. . . . . . . . . 58<br />
4.8 (a) <strong>Prediction</strong> <strong>of</strong> Figure 4.6(b) (p = 3). (b) Error between original<br />
data and predicted data. . . . . . . . . . . . . . . . . . . . . . . . . 59<br />
4.9 (a) <strong>Prediction</strong> <strong>of</strong> Figure 4.6(b) (p = 5). (b) Error between original<br />
data and predicted data. . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
4.10 (a) <strong>Prediction</strong> <strong>of</strong> Figure 4.6(b) (p = 15). (b) Error between original<br />
data and predicted data. . . . . . . . . . . . . . . . . . . . . . . . . 61<br />
4.11 Same as the data in Figure 4.6. . . . . . . . . . . . . . . . . . . . . 63<br />
4.12 2-D synthetic data for comparison <strong>of</strong> prediction between linear pre-<br />
diction theory and third order <strong>Volterra</strong> series. . . . . . . . . . . . . 65<br />
4.13 2-D synthetic data for comparison <strong>of</strong> prediction between linear pre-<br />
diction theory and the cubic part <strong>of</strong> a <strong>Volterra</strong> series. . . . . . . . . 66<br />
4.14 2-D synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67<br />
4.15 2-D synthetic data for comparison <strong>of</strong> prediction between linear pre-<br />
diction theory and a third-order <strong>Volterra</strong> series. . . . . . . . . . . . 68<br />
4.16 2-D synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69<br />
4.17 2-D synthetic data. . . . . . . . . . . . . . . . . . . . . . . . . . . 71<br />
4.18 2-D real data for comparison <strong>of</strong> prediction between linear prediction<br />
theory and a third-order <strong>Volterra</strong> series. . . . . . . . . . . . . . . . 72<br />
4.19 2-D real data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73<br />
5.1 Multiple types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77<br />
5.2 Synthetic data example. . . . . . . . . . . . . . . . . . . . . . . . . 79<br />
5.3 Synthetic data example with two multiples and one primary. . . . . 80<br />
5.4 Synthetic data example with two multiples and one primary. . . . . 81<br />
5.5 Synthetic data example with two multiples and three primaries. . . 82<br />
5.6 Real Data example. Common <strong>of</strong>fset gather. . . . . . . . . . . . . . . 84<br />
5.7 Real Data example. Common <strong>of</strong>fset gather (closer look). . . . . . . 85