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When decomposing a 1D signal with a wavelet transform into various detail levels, should I be observing autocorrelation structure in each detail that doesn't actually exist in the original signal, but somehow gets cancelled out when I add them all up to the original signal?

Normally it is natural for a filtering procedure to introduce autocorrelation structure in the filtered signal. For this reason is it possible to at least restrict the filtering for each level to be causal instead of smoothing?

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