If the ROC of X(z) is r1<|z| A |a|r1<|z|<|a|r2 B |a|r1>|z|>|a|r2 C |a|r1<|z|>|a|r2 D |a|r1>|z|<|a|r2 If the ROC of X(z) is r1<|z| Given ROC of X(z) is r1<|z| Bissoy MCQ Team Dec 01, 2024 Digital Signal Processing Properties of Z Transform Related Questions The transfer function of a discrete time LTI system is given by$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$Consider the following statements:S1 : The system is stable and causal for$$ROC:\left| z \right| > {1 \over 2}$$S2 : The system is stable but not causal for$$ROC:\left| z \right| S3 : The system is neither stable nor causal for$$ROC:{1 \over 4} Which one of the following statements is valid? A Both S1 and S2 are true B Both S2 and S3 true C Both S1 and S3 are true D S1, S2 and S3 are all true If the ROC of the system function is the exterior of a circle of radius r < ∞, including the point z = ∞, then the system is said to be ___________ A Stable B Causal C Anti causal D None of the mentioned What is the ROC of the z-transform of the signal x(n)= anu(n)+bnu(-n-1)? A |a|<|z|<|b| B |a|>|z|>|b| C |a|>|z|<|b| D |a|<|z|>|b| What is the ROC of z-transform of finite duration anti-causal sequence? A z=0 B z=∞ C Entire z-plane, except at z=0 D Entire z-plane, except at z=∞ What is the ROC of z-transform of an two sided infinite sequence? A |z|>r1 B |z| C r2<|z| D None of the mentioned The ROC of z-transform of any signal cannot contain poles. A True B False What is the ROC of a causal infinite length sequence? A |z| B |z|>r1 C r2<|z| D None of the mentioned A linear time invariant system is said to be BIBO stable if and only if the ROC of the system function _____________ A Includes unit circle B Excludes unit circle C Is an unit circle D None of the mentioned Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane. Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane. A Both A and R are true and R is the correct explanation of A B Both A and R are true bit R is NOT the correct explanation of A C A is true but R is false D A is false but R is true Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane. Reason (R): For a rational system, ROC is bounded by poles A Both A and R are true and R is the correct explanation of A B Both A and R are true bit R is NOT the correct explanation of A C A is true but R is false D A is false but R is true কোরআন চাকুরি প্রস্তুতি বিশ্ববিদ্যালয় ভর্তি মেডিকেল SBA 12 এইচএসসি 10 এসএসসি 8 জেএসসি এক্সাম দিয়ে মেধা যাচাই করুন Job Preparation (1125) Admission (754) এসএসসি (10) এইচএসসি (5)
