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Consider the following statements regarding a linear discrete-time system:
H (z) = z2+1/(z+0.5)(z-0.5)
1. The system is stable
2. The initial value of h(0) of the impulse response is -4
3. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequency
Which of these statements are correct?
H (z) = z2+1/(z+0.5)(z-0.5)
1. The system is stable
2. The initial value of h(0) of the impulse response is -4
3. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequency
Which of these statements are correct?
- a)1,2 and 3
- b)1 and 2
- c)1 and 3
- d)2 and 3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the following statements regarding a linear discrete-time sys...
Explanation: Characteristic equation is (z+0.5) (z-0.5) =0
Its root are z =0.5, -0.5
Since both roots are inside the unit circle, hence the system is stable.
Its root are z =0.5, -0.5
Since both roots are inside the unit circle, hence the system is stable.
Most Upvoted Answer
Consider the following statements regarding a linear discrete-time sys...
Explanation:
Stability:
- The given system H(z) has poles at z = -0.5 and z = 0.5.
- For a system to be stable, all poles should lie within the unit circle in the z-plane.
- In this case, both poles are inside the unit circle (|z| < 1),="" so="" the="" system="" is="" stable.="" />
Impulse Response:
- The impulse response of a system is the output when the input is an impulse function (i.e., h(0) = 1).
- Given H(z) = z^2 + 1 / (z + 0.5)(z - 0.5), the inverse Z-transform of H(z) gives the impulse response h(n).
- The initial value of h(0) is the coefficient of z^0 in the inverse Z-transform of H(z).
- By calculating the inverse Z-transform, the initial value of h(0) is found to be -4, not -43 as mentioned in the question.
Steady-State Output:
- For a sinusoidal input at a frequency equal to one-fourth the sampling frequency, the system will exhibit a steady-state response.
- The steady-state output of a linear system to a sinusoidal input at a certain frequency depends on the system's transfer function.
- In this case, the steady-state output will not be zero for a sinusoidal input at one-fourth the sampling frequency due to the system's transfer function H(z).
Therefore, the correct statements are:
- The system is stable (Statement 1)
- The steady-state output is not zero for a sinusoidal discrete-time input at one-fourth the sampling frequency (Statement 3)
Stability:
- The given system H(z) has poles at z = -0.5 and z = 0.5.
- For a system to be stable, all poles should lie within the unit circle in the z-plane.
- In this case, both poles are inside the unit circle (|z| < 1),="" so="" the="" system="" is="" stable.="" />
Impulse Response:
- The impulse response of a system is the output when the input is an impulse function (i.e., h(0) = 1).
- Given H(z) = z^2 + 1 / (z + 0.5)(z - 0.5), the inverse Z-transform of H(z) gives the impulse response h(n).
- The initial value of h(0) is the coefficient of z^0 in the inverse Z-transform of H(z).
- By calculating the inverse Z-transform, the initial value of h(0) is found to be -4, not -43 as mentioned in the question.
Steady-State Output:
- For a sinusoidal input at a frequency equal to one-fourth the sampling frequency, the system will exhibit a steady-state response.
- The steady-state output of a linear system to a sinusoidal input at a certain frequency depends on the system's transfer function.
- In this case, the steady-state output will not be zero for a sinusoidal input at one-fourth the sampling frequency due to the system's transfer function H(z).
Therefore, the correct statements are:
- The system is stable (Statement 1)
- The steady-state output is not zero for a sinusoidal discrete-time input at one-fourth the sampling frequency (Statement 3)
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Consider the following statements regarding a linear discrete-time system:H (z) = z2+1/(z+0.5)(z-0.5)1. The system is stable2. The initial value of h(0) of the impulse response is -43. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequencyWhich of these statements are correct?a)1,2 and 3b)1 and 2c)1 and 3d)2 and 3Correct answer is option 'C'. Can you explain this answer?
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Consider the following statements regarding a linear discrete-time system:H (z) = z2+1/(z+0.5)(z-0.5)1. The system is stable2. The initial value of h(0) of the impulse response is -43. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequencyWhich of these statements are correct?a)1,2 and 3b)1 and 2c)1 and 3d)2 and 3Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider the following statements regarding a linear discrete-time system:H (z) = z2+1/(z+0.5)(z-0.5)1. The system is stable2. The initial value of h(0) of the impulse response is -43. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequencyWhich of these statements are correct?a)1,2 and 3b)1 and 2c)1 and 3d)2 and 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements regarding a linear discrete-time system:H (z) = z2+1/(z+0.5)(z-0.5)1. The system is stable2. The initial value of h(0) of the impulse response is -43. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequencyWhich of these statements are correct?a)1,2 and 3b)1 and 2c)1 and 3d)2 and 3Correct answer is option 'C'. Can you explain this answer?.
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