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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

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 Correct Answer Both A and R are true bit R is NOT the correct explanation of 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. For a rational system, ROC is bounded by poles.

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?
An assertion and a reason are given below. Assertion: The phenomenon of nuclear fission generates great energy. Reason: The process in which a nucleus is broken into two parts is called nuclear fission. Choose the answer. A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion. B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. C. Both Assertion and Reason are false. D. Assertion is true but Reason is false.
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.
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,
Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Signal Processing mcq question image
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.
Consider the following statements for continuous-time linear time invariant (LTI) systems. I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. II. There is no causal and BIBO stable system with a pole in the right half of the complex plane. Which one among the following is correct?
Consider the following statements for continuous-time linear time invariant (LTI) systems.
1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
2. There is no causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?
Which of the following statements is/are true:  If f is a bijective function then f is invertible If f: A → B and g: B → C are invertible functions then g o f is also invertible function. (g o f)-1 = f-1 o g-1 
Assertion (A): Many of the linear control system transfer function do not have poles or zeroes in the right half s-plane. Reason (R): These are called minimum phase transfer function.
Direction-The question have two statements.
One is labelled as Assertion (A) and the other as Reason (R). You have to examine both the statements carefully and decide whether Assertion (A) and Reason (R) separately are true and if so then reason is the correct explanation of the assertion. Mark these items on the answer sheet.
Assertion (A): Interest payable on working capital should be treated as an item of operating expenses.
Reason (R): Interest is the cost of capital used in the business.