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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?

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? Correct Answer Both S<sub>1</sub> and S<sub>3</sub> are true

Related Questions

A stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s - 6}}.$$    To make this system causal it needs to be cascaded with another LTI system having a transfer function H1(s). A correct choice for H1(s) among the following options is
P, Q, R, S, T, W, Y and Z are sitting around a circular table from equal distances to each other and facing towards centre. They all like different colours viz., Red, Blue, Green, Black, White, Pink, Yellow and Brown (not necessarily in the same order). P likes yellow and sitting third to the left of W. Two persons are sitting between W and S. The one who likes pink is not sitting with P nor with W. Only one person is sitting between T and Z but not P and S. Y likes black but he is not sitting with S. R does not like pink nor white. T is sitting to the immediate left one who likes green. Z does not like brown nor he is sitting to the immediate right one who likes black. The one who likes white is not sitting with W. R neither likes brown nor Red. Which of the following combination is true as per the given information?
A, B, C, D, E and F are six girls who use 6 different face wash – Pond’s, Lakme, Lotus, Garnier, Himalaya and Kaya (but not necessarily in the same order). They also like six different colours – Red, Blue, Brown, Peach, Black and White (also not necessarily in the same order. A and C do not like a Red colour. The girl who uses Lakme face wash likes Peach colour. The girl who likes White colour does not use Kaya nor Lotus face wash. B neither likes Peach nor Red colour. D does not like a Blue colour but uses a Lotus face wash. The girl who uses Pond’s face wash likes Red colour. C does not use Lakme face wash nor likes white colour. F neither uses Himalaya nor Kaya face wash but likes Brown colour. Who does use Himalaya’s face wash?
Rita, Sarita, Shyam, Raj, Raman and Rahul are six different persons who are going to buy different mobiles – Nokia, Vivo, Oppo, Iphone, Jio and Xioami in different months – January to June (but not necessarily in the same order). Raj will buy Jio mobile but not in February. Sarita will neither buy Vivo mobile nor Nokia. One of the people will buy Oppo in March. Sarita will buy mobile just immediate after Raj. Rahul will buy mobile immediate before Raj. Rahul will neither buy Vivo, Oppo nor Nokia. Shyam will not buy Oppo but will buy mobile immediate after Raman. Raman will neither buy Nokia nor Iphone. Which of the following combination is not correct?
Let h(t) denote the impulse response of a causal system with transfer function $${1 \over {s + 1}}.$$  Consider the following three statements:
S1 : The system is stable.
S2 : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$  independent of t for t > 0.
S3 : A non-causal system with the same transfer function is stable.
For the above system,
A, B, C, D and E are five different persons who work in different companies - HCL, IBM, Wipro, Dell and Convergys (but not necessarily in the same order). A and D do not work in Dell. C neither works in IBM nor in HCL. E works in Wipro. B neither works in Convergys nor in Dell. D neither works in Convergys nor in IBM? Which of the following combination is not correct?
A, B, C, D, E and F are six people who like different cold drinks – Maaza, Pepsi, Coca-Cola, Sprite, Limca and Fanta (but not necessarily in the same order). Neither C nor E likes Fanta. B likes either Limca or Maaza. C does not like Pepsi. D neither likes Fanta nor Sprite. F likes Coca-Cola. C neither likes Sprite nor Limca. Which cold drink does E like?
Each item consists of six sentences of a passage. The first and sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled as P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly on the Answer Sheet. S1 : He no longer dreamed of storms, nor of women, nor of great occurrences, nor of great fish, nor fights, nor contests of strength, nor of his wife.

S6 : He urinated outside the shack and then went up the road to wake the boy.

P : He never dreamed about the boy.

Q : He only dreamed of places and of the lions on the beach now.

R : He simply woke, looked out through the open door at the moon and unrolled his trousers and put them on.

S : They played like young cats in the dusk and he loved them as he loved the boy.

The correct sequence should be
The symbols @, ©, #, $ and ⋆ are used with the following meaning illustrated. X @ Y → X is not greater than Y, X © Y → X is neither smaller than nor equal to Y, X # Y → X is neither greater than nor smaller than Y, X $ Y → X is not smaller than Y, X * Y → X is neither equal to nor greater than Y. Statements: A # B $ C * D, C * E $ F, D * F, E @ J Conclusion: I. J © C II. F * J
P, Q, R, S, T and U are six persons who have different mobiles - Nokia, Vivo, Oppo, Samsung, Apple and Jio (but not necessarily in the same order). P does not have Apple mobile. U does not have Oppo nor Vivo mobile. T has a Nokia mobile. R does not have Oppo nor Apple mobile. Q does not have Samsung nor Oppo mobile. P does not have Oppo nor Jio mobile. U does not have Jio nor Apple mobile. Which of the following combinations is correct?