The transposition theorem says that if we take a filter diagram and reverse all the elements  swapping the order of execution for every element, and reversing the direction of all the flow arrows  then the result is the same:
This means that the direct form 1 diagram can be obtained by transposition of the direct form 2 diagram: For this reason, direct form 1 is often called transposed direct form 2. Don't ask me why these terms seem to be as confusing as they possibly could be  I didn't make them up. I imagine mathematicians sit around at coffee break and come up with new ways to spread despondency amongst us lesser mortals. Here are the two main sources of confusion:
