Hi Simon, that energy normalization should be interpreted here in the correct way. With the CWT, we don't preserve the energy in either case with the L1 or L2 normalization. That energy preservation is only in the integral form of the CWT which is not implemented numerically. The same is true of the spectrogram in the Signal Processing Toolbox. If you look at the integral forms for the CWT with the L2 normalization, then the energy is preserved. However, when you implement the CWT numerically, that is not the case. We will make that clear in the documentation.
现在，在DWT的情况下，具有非常具体的条件，即，当我们以两个输入功率和信号长度实现经典DWT时，有两个功率。您将看到保留的能量。例如：
dwtmode('每')
x = randn（1024,1）;
norm（x，2）^2
[c，l] = wavedec（x，10，'sym4'）；
norm(C,2)^2
But that won't happen with the CWT (by design) and it has nothing to do with the L2 vs L1 normalization. In fact if you look at the legacy CWT, we didn't preserve signal energy there either even though the wavelets were normalized by 1/\sqrt{s}.
If you want a redundant wavelet or wavelet packet transform that does preserve the energy, then MODWT and MODWPT will do that. They are what are referred to as "tight wavelet (and wavelet packet) frames".
同样，CWT中L1归一化的原因是，如果您的数据在不同尺度上具有相等的振幅振荡组件，则它们在CWT中应具有相等的幅度，并且不会乘以量表因子。
