Discrete-time Systems and Pole-Zero Analysis
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Questions and Answers

What is the primary purpose of the Z-transform in discrete-time systems?

  • To convert algebraic equations into difference equations
  • To convert difference equations into algebraic equations (correct)
  • To design continuous-time systems
  • To analyze the time response of discrete-time systems

    • What do poles in a discrete-time system represent?

  • The frequencies with zero magnitude response
  • Frequencies that are completely attenuated by the system
  • The resonant frequencies of the system (correct)
  • The frequencies with infinite magnitude response

    • What happens if a discrete-time system has a pole outside the unit circle?

  • The system becomes unresponsive
  • The system becomes more stable
  • The system becomes unstable (correct)
  • The system becomes oscillatory

    • What is the frequency response of a discrete-time system?

    <p>A plot of the magnitude and phase of the system's transfer function versus frequency</p> Signup and view all the answers

    What do zeros in a discrete-time system represent?

    <p>Frequencies that are completely attenuated by the system</p> Signup and view all the answers

    What is the condition for a discrete-time system to be stable?

    <p>All poles are inside the unit circle</p> Signup and view all the answers

    Study Notes

    Discrete-time Systems

    • The Z-transform is a powerful tool for analyzing discrete-time systems, which are systems that process discrete-time signals.
    • Discrete-time systems can be represented by difference equations, which describe the relationship between input and output signals.
    • The Z-transform is used to convert difference equations into algebraic equations, making it easier to analyze and design discrete-time systems.

    Pole-Zero Analysis

    • Pole-zero analysis is a method of analyzing the frequency response of a discrete-time system using the Z-transform.
    • Poles:
      • Defined as the values of z that make the transfer function infinite.
      • Represent the resonant frequencies of the system.
      • A system with poles close to the unit circle will have a large response to certain frequencies.
    • Zeros:
      • Defined as the values of z that make the transfer function zero.
      • Represent the frequencies that are completely attenuated by the system.
    • Stability:
      • A system is stable if all poles are inside the unit circle.
      • A system is unstable if any pole is outside the unit circle.
    • Frequency Response:
      • The Z-transform can be used to find the frequency response of a discrete-time system.
      • The frequency response is a plot of the magnitude and phase of the system's transfer function versus frequency.

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    Description

    Learn about discrete-time systems, Z-transform, pole-zero analysis, and frequency response. Understand how to analyze and design discrete-time systems using difference equations and Z-transform.

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