As explained in section 6.2, the discrete multiwavelet transform (DMWT) is based on the decomposition
A function can be expanded either as
(and likewise for ), and
The multiscaling and multiwavelet functions are column vectors. The coefficients are row vectors. The notation s, d originally stood for sum and difference, which is what they are for the Haar wavelet.
You can also think of them as standing for the smooth part and the fine detail of s. The original function s (x) is the signal.