Question

1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression for determining the gain factor in part b to match the above specs

Answer 1

olotion:- a) Note in the given diagam that he Mees is highest at A+阴12 and -p?la- it is zeso at =0 and at and the 2esos have to be placed at o o ond at p? and the poles at ω=p?12 and -P12 he pole - 2eso plois belou P Thus, ㄟ 2. b) sinte the poles ase at and ond the zesos at spes Punction is l and-〉,the

amplitude ís 1.at ฟ=p?/2, p?/2, 1HC2.)l=KX(2) . since C) Since the maXimUm omp maximum we see that at ke l/2 the/gan have 包.2kel,We