how to compute the energy of each node of the wavelet packet tree?
in [Matlab]
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From: John Ramshur on 7 Feb 2010 03:27 I have an additional question. I've noticed in journal articles for my field calculating wavelet packet energy using two different methods. They use one of the two methods below. 1. E=sum(abs(WpCoeffsNode3).^2) 2. E=sqrt(1/N*sum(abs(WpCoeffsNode3).^2)) %RMS method So what's the correct way?
From: Wayne King on 7 Feb 2010 09:00 "John Ramshur" <jramshur(a)gmail.com> wrote in message <hkltgm$hrf$1(a)fred.mathworks.com>... > I have an additional question. > > I've noticed in journal articles for my field calculating wavelet packet energy using two different methods. They use one of the two methods below. > > 1. E=sum(abs(WpCoeffsNode3).^2) > > 2. E=sqrt(1/N*sum(abs(WpCoeffsNode3).^2)) %RMS method > > So what's the correct way? Hi, John, I think they're both "correct" since they are both giving a measure of the wavelet packet energy. Which one is most appropriate in your application depends on what you are using the wavelet packet decomposition for. The first is just the squared norm. You could also easily take the square root of that and use the norm. The RMS is dividing the squared norm by the number of coefficients (values) and taking the square root of that. So the RMS will control for the different number of coefficients at different levels of the wavelet packet tree--in that sense it would give you perhaps a fairer comparison between levels because you have more coefficients (in a decimated WPT) at higher levels of resolution. The RMS is also a statistical expectation since you are using the factor 1/N as an expected value. So if you are using wavelet packets to characterize a stochastic process, the RMS may be more appropriate for example. Hope that helps, Wayne
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