Re: DWT anti-causality

lucas.denoir@xxxxxxxxx wrote:
Jerry Avins wrote:

The filter delay is built into the problem; low frequencies at high
sample rates make for long filters. Downsampling the data is simply an
efficient way to downsize the filter. Using a different filter that
enables you to avoid downsampling won't decrease your delay.

Put differently, you can either downsample the data or increase the
filter length for each pass. That increases memory use but doesn't
change the delay.


Right - I'll end up doubling the filter length for each level and end
up with the same situation. Ok, scratch that idea.

How about my initial one, that didn't work - simply using an expanding
window? For each sample you transform it and the previous samples. You
then only keep the last sample from each transform. I know it is
computationally atrocious, but still, it should eliminate the delay, at
least explicitly. It didn't work for me (i suspect) because of the
boundary problems due to padding, but I'm thinking it's possible to
work around the problem by using such window lengths that no padding is
necessary. In that situation, there will be a delay, but it will be
constant for all decomposition levels.

Low frequencies at high data rated demand long filters. Long transforms are needed to get to low frequencies with the proposed scheme. It's true that aside from startup and ending transients there is a sample out for each sample in (self evident, really), but you need to ask how long before an input sample significantly affects the output. If your transforms have a few kilosamples of history in them, and every sample matters, there's your delay. FFT or FIR; the computations are different but equivalent. The delays are precisely the same.

BTW, a sliding FFT, which is what you just described, needn't be inefficient. Google it.

Jerry
--
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