Translations:Prediction-error filters/14/en

Let us give an example of a case in which the input wavelet is a minimum-delay wavelet. In any deconvolution problem, the first thing to do is to compute the unit-distance prediction-error filter (i.e., the normalized spiking filter). The inverse of the normalized spiking filter gives the minimum-delay wavelet. Figure 3a (left) shows the minimum-delay input and Figure 3a (right) shows the desired output for the case of 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 n = –1. Figure 3b (left) shows the unit-distance prediction filter, and Figure 3b (right) shows the prediction. Note that the values for nonnegative times agree well with the desired output. On the other hand, values of the desired output for negative times cannot be reached by the filter. These values give the so-called unreachable prediction error, which for the case of unit prediction distance is simply a spike. Figure 3c (left) shows the unit-distance prediction-error filter, and Figure 3c (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).