Prediction filter templates

My new DAMF prediction filters are three dimensional. The locations of filter coefficients in the midpoint-offset space is shown in the mask below:

     .00     .00     .00    2.00     .00     .00     .00
    1.00     .00     .00     .00     .00     .00     .00
    1.00    1.00     .00     .00     .00     .00     .00
    1.00    1.00    1.00     .00     .00     .00     .00
    1.00    1.00    1.00    1.00     .00     .00     .00
    1.00    1.00    1.00    1.00    1.00     .00     .00
    1.00    1.00    1.00    1.00    1.00    1.00     .00
    1.00    1.00    1.00    1.00    1.00    1.00    1.00
    1.00    1.00    1.00    1.00    1.00    1.00    1.00

In the above mask, the vertical axis is midpoint and the horizontal is offset. Where the mask contains a zero, the filter coefficient is constrained to zero. Where the mask contains ``1.00'', the filter coefficient is free, both in this filter plane and in planes above and below which filter on the time axis. Where the mask contains ``2.00'' the filter coefficient is constrained to be ``1.00'' in this plane and zero in other planes.

Kjartansson's filter, by comparison, lies on one time slice. It is a ``1.00'' on the predicted point and -1/47 on each of the other traces at this midpoint.

Figure 6 shows the zero lag crosscorrelation of data with its prediction. Naturally, the crosscorrelation is sensitive to amplitude as well as timing, so the crosscorrelation at zero lag is shown before and after normalization. Naturally also, the crosscorrelation need not be positive, but tends to be positive (since we are correlating a signal with its prediction) so I had a little trouble getting the brightness adjusted suitably for plotting.

 

xcorr
Figure 6 Zero lag crosscorrelation of data with its prediction. Top without normalization. Bottom with normalization. Amplitude normalization means the display is sensitive to time shifts. Press button for movie cube.