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We have seen that the output at any stage is
produced by a sequence of identical
filtering and decimating operations. An alternative algorithm is to calculate
the single long filter and the single multiple decimation that would
produce exactly the same result. Here we are not operating on data
but on the wavelet filters themselves. At each stage, the new low-pass filter
is the old low-pass filter convolved with the basic low-pass filter decimated
by a factor of 2^{n}, where *n* is the stage. Similarly the new high-pass
filter is the old low-pass filter convolved with the multiply-decimated
basic high-pass filter.

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Stanford Exploration Project

11/17/1997