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Part of my assignment about signal processing says the following:

  • Compute the Discrete Wavelet Transform for the input signals
  • Group the wavelet coefficients in trees growing across scales
  • Classify the trees in high- and low-energy trees

I've managed to implement my own DWT, calculate the coefficients and group them in trees.

Now I'm left with calculating the energy of the wavelet coefficients.

Question: How to calculate the energy of wavelet coefficients?

I am doing this in Matlab.

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If such coefficients are calculated from an orthonormal basis, rather than from a redundant wavelet transform like the discrete case of a CWT, then the energy is the sum of the square of the absoute values of those coefficients, because orthonormal wavelet bases converge in norm, and the energy of a signal is defined as the integral of its absolute value. See https://en.wikipedia.org/wiki/Energy_(signal_processing)

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