GATE ECE 2018: Discrete Time Signal Z Transform Question

Key Concepts

• Discrete Time All-Pass System:
  • System with poles at specific values, particularly 0.250 and 30 in this context.
  • Question involves determining the truth about the system from given options.

Question Analysis

• Options for System Characteristics:

  • Option A: Two more poles at 0.530 and 40.
  • Option B: Stability when impulse response is two-sided.
  • Option C: Constant phase response over all frequencies.
  • Option D: Constant phase response over the entire z-plane.

• Correct Answer: Needs to be determined based on the system properties.

Related Concepts

• Z-Transform:

  • A mathematical tool used for analyzing discrete time signals.
  • Region of convergence (ROC) is crucial in determining system stability and characteristics.

• Impulse Response:

  • Describes how a system responds to a discrete-time impulse input.

Important Notes:

• Stability Criteria:

  • Stability of a discrete-time system is dependent on the location of poles relative to the unit circle in the z-plane.

• Phase Response:

  • An all-pass system could potentially maintain a constant phase response, but specifics depend on the pole-zero configuration.

Other Relevant Past Questions

• Examples include questions from GATE ECE 2016 and 2015, focusing on similar topics such as poles, impulse response, z-transform properties, and ROC.

• GATE ECE 2016:

  • Question focusing on the sequence and its z-transform convergence.

• GATE ECE 2015:

  • Numerical question involving finding the value of x[2] given its z-transform.

Study Tips

• Focus on understanding the properties of poles and zeros in the z-plane.
• Practice questions involving stability and phase response of systems.
• Review the concepts of z-transform and its application to signal processing.