Hi,
By number of degrees of freedom we mean: the number of independent ways (variables) the filter can vary its output without violating all the constraints that we have imposed on the filter. Mathematically it means, the number of the dimensions of the domain of a random vector i.e. the number of "free" components (how many components need to be known to fully determine the vector (system)).
I hope this would help explaining your answer to some extent.
Thanks
TA