Transposed Direct Form II VS Direct Form II IIR filters? I read in "Discrete-Time Signal Processing" Reference, in transposed Direct Form II filters section, that it implements zeros first then poles(unlike Direct form II which implements poles first), Which is important in the presence of quantization of finite precision or noise without adding further explanation.

Why implementing Zeros first is better than implementing poles first?
Compared to the Direct Form I, Direct Form-II has pros and cons.


The advantage of DF-II is its more efficient usage of the delay lines. Although both use separate all-pole and all-zero sections, the DF-II can share the delay lines between them and reduce the number of required delays to implement the same transfer function.
The disadvantage of DF-II is that it precedes the poles and imposes a higher dynamic range on the intersecting delay line in some frequencies. Therefore, unlike the DF-I which first implements the zeros and is almost immune to overflow, DF-II is prone to such effects.


In the transposed DF-II the zeros are implemented first AND the delay lines are shared between the all-pole and the all-zero section. Hence, the transposed DF-II has the advantage of DF-II and also offers a better robustness similar to the behavior of DF-I.

Also, it is stated here that they are more robust when filters with a sharp-transition are implemented.