GATE EC 2014 Set 3 — Question 53

NAT+2 / -0MediumPoles & ZerosLTI SystemsSignals & Systems

Signals & Systems → LTI Systems → Poles & Zeros

Last updated 5 September 2026

Question

H_1(z) = (1 - pz^{-1})^{-1}

H(z) = H_1(z) + r H_2(z) = \frac{1}{1 - pz^{-1}} + \frac{r}{1 - qz^{-1}}

Review answer and solution without JavaScript

Interactive answer checking needs JavaScript. The published solution is available below.

H(z) = H_1(z) + r H_2(z) = \frac{1}{1 - pz^{-1}} + \frac{r}{1 - qz^{-1}}

Continue learning with Success Tracker

Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans

PYQs with solutions: Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts: Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support: Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.