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We can use the same technique to throw out fitting equations from defective data that we use for missing data. Recall the theory and discussion leading up to Figure [*]. There we identified defective data by its lack of continuity. We used the fitting equations $0\approx w_i (y_{i+1} -2y_i + y_{i-1})$where the weights wi were chosen to be approximately the inverse to the residual (yi+1 -2yi + yi-1) itself.

Here we will first use the second derivative (Laplacian in 1-D) to throw out bad points, while we determine the PEF. Having the PEF, we use it to fill in the missing data. pefestestimate PEF in 1-D avoiding bad data The result of this ``PEF-deburst'' processing is shown in Figure [*].

Figure 5
Top is synthetic data with noise spikes and bursts. (Some bursts are fifty times larger than shown.) Next is after running medians. Next is Laplacian filter Cauchy deburst processing. Last is PEF-deburst processing.

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Given the PEF that comes out of pefest1()[*], subroutine fixbad1() below convolves it with the data and looks for anomalous large outputs. For each that is found, the input data is declared defective and set to zero. Then subroutine mis1() [*] is invoked to replace the zeroed values by reasonable ones. fixbadrestore damaged data