Chart-function relations

For example, the coefficient array with $c_{10}=q$, $c_{00}=1$, and all other entries zero is a nonzero array with zero reconstruction whenever both indices are permitted. Similarly, the array with $c_{00}=r^2$ has zero reconstruction. These statements exhibit dependence of the reconstructed family over chart functions.

They do not say that the frequency amplitude module itself has the same relation. In particular, $(qi\theta +1)M_{\mathrm{R}}$ is a nonzero frequency presentation whose physical reconstruction vanishes. This is exactly why polynomial degree is a degree of a presentation and cannot by itself define an intrinsic filtration of a reconstructed joint symbol.