I check in this wikibook page - https://en.wikibooks.org/wiki/Control_Systems/Block_Diagrams and from the transformation "Moving a Summing Junction in front of a Block", it says to add a 1/P block, which in this case would be a differentiator. I tried adding a differentiator block like below, but the outputs (taken @ every 100th clock cycle) of the blocks does not match. (MODEL-2)
The output from MODEL-1 is:
The output from MODEL-2 is:
This is one part of this question.
However the major part is, when using this filter practically, the input to this filter contains high-frequency noise(now - just for example, it contains a pure sinusoid). By adding a differentiator in the front for the purpose of transformation dissolve the whole purpose of filtering?