Translations:Tail shaping and head shaping/11/en

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Let us interpret this equation in terms of the prediction-error filter. Because the desired output is the first values of the minimum-phase wavelet, the crosscorrelation is the autocorrelation of the head. Because the head is of length , the crosscorrelation vanishes for lags greater than . The input wavelet is minimum phase. The prediction-error operator shortens this input wavelet b to its head, which is of length . Because is an independent variable, we are free to select whatever value we wish for . Thus, we can control the desired degree of resolution or wavelet contraction. However, this use of the prediction-error filter is not a more generalized approach to deconvolution but is part of a unified whole. The set of prediction-error filters (with various prediction distances) for a given autocorrelation has the spiking filter (which has prediction distance 1) at one extreme and the do-nothing filter (with prediction distance ) at the other extreme. All of the prediction-error filters in the set are simply related to each other.