Translations:Prediction-error filters/16/en

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Let us now give an example of a case in which the input wavelet is a mixed-delay wavelet. Figure 4a (left) show a nonminimum-delay input with the same autocorrelation as that of the minimum-delay input wavelet in Figure 3a (left). This nonminimum-delay input wavelet is obtained by passing the minimum-delay wavelet through an all-pass filter. We proceed as before. Figure 4a (right) shows the desired output for unit prediction distance. This desired output is the wavelet advanced by one time unit to the left — that is, the first nonzero coefficient of the desired output occurs at negative time . Figure 4b (left) shows the unit-distance prediction filter, which is the same as that in Figure 3b (left). Figure 4b (right) shows the prediction. Now, however, we note that the values for nonnegative times no longer agree with the desired output, as was the case for the minimum-delay input. On the other hand, the filter cannot reach the values of the desired output for negative times. These values give the so-called unreachable prediction error, which for the case of unit prediction distance is simply a spike. Figure 4c (left) shows the prediction-error filter, which is the same as that in Figure 3c (left). Figure 4c (right) shows the difference between the desired output and the prediction. The output of the prediction-error filter is this difference delayed by one time unit (i.e., by the prediction distance).