Question

By combining two pairs of poles to form a fourth order filter section, by what factor we have reduced the number of multiplications?

(a) 25%

(b) 30%

(c) 40%

(d) 50%

The question was posed to me in final exam.

The doubt is from Structures for FIR Systems in chapter Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Right answer is (d) 50%

To explain I would say: We have to do 3 multiplications for every second order equation. So, we have to do 6 multiplications if we combine two second order equations and we have to perform 3 multiplications by directly calculating the fourth order equation. Thus the number of multiplications are reduced by a factor of 50%.