A MATLAB implementation of the scattering transform is available with support for Cosine Log-Scattering (CLS) coefficients.
If you find any bugs or have any questions, please contact Joakim at the address below.
The scattering coefficients of up to order 2 were computed for a 6-second clip of classical music for for different window sizes (20ms, 400ms, 740ms, 1.5s and 4s). These coefficients were then used to reconstruct the original signal, first using only the first-order coefficients, and then using the first and second order. The results are as follows
Note that although the reconstruction is of good quality for m=1 when T is small, it deteriorates significantly when T increases. However, if we add the second order, quality is restored, especially with respect to transients such as attacks. For even larger values of T, however, the quality of the reconstruction for m=2 suffers as well.