Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > An IIR system with system function H(z)=(B(z)...
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An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixed phase if:
- a)All poles and zeros are inside the unit circle
- b)All zeros are outside the unit circle
- c)All poles are outside the unit circle
- d)Some, but not all of the zeros are outside the unit circle
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixe...
Explanation: For an IIR filter whose system function is defined as H(z)=(B(z))/(A(z)) to be said a mixed phase and if the system is stable and causal, then the poles are inside the unit circle and some, but not all of the zeros are outside the unit circle.
Most Upvoted Answer
An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixe...
Definition of a Mixed Phase IIR System
A mixed phase IIR (Infinite Impulse Response) system is a type of filter where some, but not all, of the zeros are located outside the unit circle in the z-plane. The system function of a mixed phase IIR system is given by:
H(z) = (B(z))/(A(z))
Where B(z) and A(z) are the numerator and denominator polynomials of the system function, respectively.
Explanation of the Correct Answer
The correct answer is option 'D': Some, but not all of the zeros are outside the unit circle. This means that in a mixed phase IIR system, there are both zeros inside and outside the unit circle.
Reasoning
To understand why option 'D' is correct, let's examine the properties of the poles and zeros in the z-plane.
Poles:
- Poles are the values of z for which the denominator polynomial A(z) becomes zero.
- Poles can be either inside or outside the unit circle.
- If all poles are inside the unit circle, the system is stable and has a causal response.
- If any poles are outside the unit circle, the system is unstable and has an anti-causal response.
Zeros:
- Zeros are the values of z for which the numerator polynomial B(z) becomes zero.
- Zeros can also be either inside or outside the unit circle.
- If all zeros are inside the unit circle, the system is causal and has a minimum phase response.
- If any zeros are outside the unit circle, the system is non-causal and has a maximum phase response.
A mixed phase IIR system:
- Combines the properties of both causal and non-causal systems.
- Has some poles inside and some poles outside the unit circle.
- Has some zeros inside and some zeros outside the unit circle.
Therefore, option 'D' is the correct answer because it accurately describes a mixed phase IIR system where some, but not all of the zeros are located outside the unit circle.
A mixed phase IIR (Infinite Impulse Response) system is a type of filter where some, but not all, of the zeros are located outside the unit circle in the z-plane. The system function of a mixed phase IIR system is given by:
H(z) = (B(z))/(A(z))
Where B(z) and A(z) are the numerator and denominator polynomials of the system function, respectively.
Explanation of the Correct Answer
The correct answer is option 'D': Some, but not all of the zeros are outside the unit circle. This means that in a mixed phase IIR system, there are both zeros inside and outside the unit circle.
Reasoning
To understand why option 'D' is correct, let's examine the properties of the poles and zeros in the z-plane.
Poles:
- Poles are the values of z for which the denominator polynomial A(z) becomes zero.
- Poles can be either inside or outside the unit circle.
- If all poles are inside the unit circle, the system is stable and has a causal response.
- If any poles are outside the unit circle, the system is unstable and has an anti-causal response.
Zeros:
- Zeros are the values of z for which the numerator polynomial B(z) becomes zero.
- Zeros can also be either inside or outside the unit circle.
- If all zeros are inside the unit circle, the system is causal and has a minimum phase response.
- If any zeros are outside the unit circle, the system is non-causal and has a maximum phase response.
A mixed phase IIR system:
- Combines the properties of both causal and non-causal systems.
- Has some poles inside and some poles outside the unit circle.
- Has some zeros inside and some zeros outside the unit circle.
Therefore, option 'D' is the correct answer because it accurately describes a mixed phase IIR system where some, but not all of the zeros are located outside the unit circle.
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An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixed phase if:a)All poles and zeros are inside the unit circleb)All zeros are outside the unit circlec)All poles are outside the unit circled)Some, but not all of the zeros are outside the unit circleCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixed phase if:a)All poles and zeros are inside the unit circleb)All zeros are outside the unit circlec)All poles are outside the unit circled)Some, but not all of the zeros are outside the unit circleCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixed phase if:a)All poles and zeros are inside the unit circleb)All zeros are outside the unit circlec)All poles are outside the unit circled)Some, but not all of the zeros are outside the unit circleCorrect answer is option 'D'. Can you explain this answer?.
An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixed phase if:a)All poles and zeros are inside the unit circleb)All zeros are outside the unit circlec)All poles are outside the unit circled)Some, but not all of the zeros are outside the unit circleCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixed phase if:a)All poles and zeros are inside the unit circleb)All zeros are outside the unit circlec)All poles are outside the unit circled)Some, but not all of the zeros are outside the unit circleCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An IIR system with system function H(z)=(B(z))/(A(z)) is called a mixed phase if:a)All poles and zeros are inside the unit circleb)All zeros are outside the unit circlec)All poles are outside the unit circled)Some, but not all of the zeros are outside the unit circleCorrect answer is option 'D'. Can you explain this answer?.
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