In the attached document for 2nd order sigma delta, we have used up down counter approach to implment filter section (page 738 and 739)

the filter stage1 after comparator 1 uses  x = x + xx * (n - i +1)
where xx is comp1 output and x is output of filter and  1<i <n

the filter stage2 after comparator 2 uses  y = y + yy
where yy is comp2 output and y is output of filter2 and  from summation 1 to n

Now wat i interpret is that in filter 1 there are two stages in series of up-down counters and in filter2 there is only one stage of up down counter.
what does this term (n - i +1) means what is the significance. Does it signify the order of filter?
how to increase order of these two filters?
How can i make the three stage filter from up down counter using above equations
any clue about this will be helpful !!

thanks