Dear list members
I'll appreciate your feedback on this point regarding the wavelet
analysis and moving averages.
In many books on wavelets, one of the most frequent images used to
describe the potentialities
of wavelets analysis is an image of a signal with superposed the wavelets
coefficients for different levels of resolution.
From what I see, similar results could be obtained simply
applying moving averages at different scales and differentiating
neighboring scales. For example if have a signal discretized in 1024
points, I could
calculate moving averages with windows of 4 (w4),8 (w8),16 (w16),
32(w32) points and do the differences:
w4-w8, w8-w16, w16-w32.
From what I have seen (for the signals that I analyzed) the results,
at least visually, are really similar to wavelet coefficients at
different levels of resolution.
So, I'm directed to think that for an explorative analysis of data
a simple moving average technique could be preferred (except in the
case in which I have some
reason to use a specific form of wavelet). Clearly I understand that
for other tasks (edge detection, signal compression, etc...)
we need wavelets.
I'm wrong???
Thank you in advance for your replies.
Sebastiano T.
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