Re: DWT anti-causality

lucas.denoir@xxxxxxxxx wrote:

Apart from extending a window, I can think of another method:
fake-extending the signal. The basic idea being that I pad the signal
(symmetric extension or something like that) with the length of the
maximum needed delay for the original signal. I then do the transform
and and pick my sample from its original point in time, ignoring the
extended samples. I haven't tried it yet, but I suspect I'll end up
with the same results as with the expanding window...

Symmetric extension at the edges is a pretty common technique in
wavelet decomposition. Waving my hands wildly, it seems to me that
doing this nets twice the coefficient variance as for central
coefficients that use complete input data. Proof left to the reader, of
course.

Another approach would be to switch to asymmetric basis functions at
the edges. That's a time-honored technique with conventional spline
fitting. Poking through the literature on spline wavelets might yield
something applicable.

Third idea is forget about using the coefficients that are too close to
the boundary. If new data keeps coming in, all you have to do is wait.
For years, folks have been using overlap techniques with FFT's to
reduce blocking problems. What keeps you from doing the same thing with
the DWT?

David L. Rick
Hach Company

Note: The address in the header goes straight to the bit bucket. Actual
humans are welcome to contact me at
davidDOTrickAThachDOTcomREMOVE

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