Please help me understand this paper about Discrete Wavelet Transform!
Basically, the method decomposes a signal into one approximation $A_7$ and seven details $D_7$,..., $D_1$. Since the wavelet is orthogonal, the energy of the signal is equal to the sum of the energy of each subband. To me, equation (1) is not correct, one should not sum approximations over levels. Approximation coefficients $A_7$ are discarded, they kind of remove the low frequency or baseline parts. They keep the four most energetic detail subbands, which they order by decreasing energy. Then they set the others to zero, and reconstruct the signal by inverse wavelet transform. So no level is missing, they are just erased. This turns out to be a very crude form of denoising, as they finally only keep the central frequencies, in the interval $[1/2^7\; 1/2^3]$. This could be a misuse of wavelets, as a simple bandpass filter could have been better.