An IIR system with system function H(z)=(B(z))/(A(z)) is called a mini...
Explanation: For an IIR filter whose system function is defined as H(z)=(B(z))/(A(z)) to be said a minimum phase,
then both the poles and zeros of the system should fall inside the unit circle.
View all questions of this test
An IIR system with system function H(z)=(B(z))/(A(z)) is called a mini...
Understanding Minimum Phase Systems
A minimum phase system is characterized by its pole-zero configuration in the z-plane. The key features of such systems are essential for stability and performance in signal processing.
Definition of Minimum Phase
- A system is classified as minimum phase if:
- All zeros of the system function H(z) are located inside the unit circle.
- All poles of the system function H(z) are also located inside the unit circle.
Reasoning Behind Option 'A'
- Stability:
- For a system to be stable, all poles must be within the unit circle. This ensures that the system's response does not grow unbounded over time.
- Causality:
- A minimum phase system is causal, meaning its output depends only on current and past inputs, which aligns with poles being inside the unit circle.
- Phase Characteristics:
- The phase response of a minimum phase system is the least phase shift for a given magnitude response. This is crucial in applications like filtering, where phase distortion can be detrimental.
- Energy Consideration:
- A minimum phase system tends to have a more efficient energy response, as energy is not lost due to excessive phase shifts.
Conclusion
In summary, for H(z) to be a minimum phase system, both poles and zeros must be inside the unit circle. This ensures stability, causality, and optimal phase characteristics, making option 'A' the correct answer. Understanding this principle is vital for effective system design in electrical engineering.