MATLAB: What is the difference between scalogram and scatteing coeffcients?

Question

figure

scattergram(sf,U,'FilterBank',1)

What's the difference between scalogram and scatterinf coefficients ?

Also, why can I only choose a number between 0 and 2 as the 'FilterBank' value?

I ahve been reading documentation for a while but I do not quite understand the answer provided in the wavelet transform page.

I would like to know which part of the signal the coefficients represent and what is the difference between the two types of coefficients.

Thanks!

Answer 1

1. Consider a 1-D signal F. The zeroth order scattering coefficient can be obtained by convolving F with the scaling function  to obtain S[0], the low frequency components at level 0. To obtain the high frequency components. we convolve F with the filter bank coefficients , where j is the level and k is the filter bank index, and take modulus of the outputs to extract 1st order scalogram coefficients U[1] or the high frequency components at level 1. To obtain the low frequency components at level 1, one can convolve the modulus values with the scaling function  to obtain the values S[1]. In this way we keep breaking down the signal and keep repeating the process at each level. The scalogram coefficients U extract the high frequency or detailed components, while the scattering coefficients S extract the low frequency components at every level of resolution.
2. The 'FilterBank' value depends on the waveletScattering object sf. Changing the sf object changes the number of filter banks.

You can go through the following documentation link for further help:

https://www.mathworks.com/help/wavelet/ug/wavelet-scattering.html