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Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

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4.3. NONLINEAR PREDICTION OF COMPLEX WAVEFORMS 54<br />

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(a)<br />

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Figure 4.3: (a) <strong>Prediction</strong> <strong>of</strong> Figure 4.2(b) (p = 3). (b) The error between original<br />

data and predicted data.<br />

signals. It is clear that linear prediction will fail in modeling such events. A solution<br />

to the problem is to use linear prediction techniques in small windows or to resort<br />

to nonstationary linear prediction operators (Sacchi and Kuehl, 2001).<br />

I chose a 2-D synthetic data example consisting <strong>of</strong> 5 different hyperbolic events.<br />

The example does not satisfy the f − x assumption <strong>of</strong> constant ray parameter<br />

waveforms in the t − x domain. In this case I do not have a superposition <strong>of</strong><br />

complex exponentials in the f − x domain. Therefore the minimum value for the<br />

filter length (p = 5) in Figure 4.7(a) will be an approximated value for the hyperbolic<br />

event presented in Figure 4.6(b). Again, the data in Figure 4.6(a) is contaminated<br />

(b)

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