Topic: Signals and Systems
Consider the compound system shown in below figure. Its output is equal to the input with a delay of two units. If the transfer function of the first system is given by H1(Z) = (Z - 0.5)/(Z - 0.8), then the transfer function of the second system H2(Z) is
- A. H2(Z) = (Z^-2 - 0.2Z^-3)/(1 - 0.4Z^-1)
- B. H2(Z) = (Z^-2 - 0.8Z^-3)/(1 - 0.5Z^-1)
- C. H2(Z) = (Z^-1 - 0.2Z^-3)/(1 - 0.4Z^-1)
- D. H2(Z) = (Z^-2 - 0.8Z^-3)/(1 - 0.5Z^-1)
Answer: B. H2(Z) = (Z^-2 - 0.8Z^-3)/(1 - 0.5Z^-1)
Explanation: The overall transfer function is a delay of two units, so H(Z) = Z^-2. Since H(Z) = H1(Z) * H2(Z), H2(Z) = Z^-2 / H1(Z) = Z^-2 * (Z - 0.8)/(Z - 0.5). Multiplying numerator and denominator by Z^-1 yields (Z^-2 - 0.8Z^-3)/(1 - 0.5Z^-1).