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From Continuous Time System to Discrete Time System

From Continuous Time System to Discrete Time System . ES400 Jack Ou, Ph.D. Chapter 1. Outline. Modeling Signal System Continuous Time System ADC Discrete Time System. Signals. Signals are divided into two natural categories

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From Continuous Time System to Discrete Time System

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  1. From Continuous Time System to Discrete Time System ES400 Jack Ou, Ph.D. Chapter 1

  2. Outline • Modeling • Signal • System • Continuous Time System • ADC • Discrete Time System

  3. Signals • Signals are divided into two natural categories • Continuous time signal: Discrete time signal: defined at only defined for all values of time • Discrete Time Signal: Only defined at certain instants of time.

  4. Example of a Continuous Time Signal • Criterion: The signal defined for all values of time • Techniques: Fourier series, Fourier transform, Laplace transform

  5. Example of a Discrete Time Signal • Criterion: The signal is defined for at only certain instants of time • Technique: Z transform, DFT, FFT

  6. Tinkering

  7. Mathematical Modeling of a Physical System

  8. Mathematical Solutions of Physical Problems Formulate a math model for physical signal and system involved. Equations are solved for typical excitation function. Compare math solution with the response of the physical system Iterate the process until close correlation between the measured and model is achieved.

  9. Continuous Time Example

  10. Mathematical Modeling of Elementary Circuits

  11. Use KVL to formulate the mathematical representation of a physical system • KVL: The algebraic sum of Voltages around any closed loop in an electric circuit is zero.

  12. Describe the input signal mathematically

  13. Represent Input Voltage Source using Laplace Transform

  14. Solve the problem in the Laplace Domain • Laplace transform the KVL expression • Solve the variable of interest • Inverse Laplace Transform

  15. Not All Systems Can Be Represented Using a Continuous Time Representation

  16. Convert a Signal From Continuous Time System to Discrete Time System • Operational Amplifier • Digital to Analog Converter • Comparator • Counter-Ramp Analog to Digital Converter

  17. Operational Amplifier If used in a feedback configuration, V+=V-. Large input impedance!

  18. A Simple Voltage Amplifier

  19. Digital-to-analog Converter Purpose: Convert a binary number to a voltage.

  20. A Simple Digital to Analog Converter Assume “1”=5V, “0”=0V D0=“1”, D1=“0”, D2=“0” What is Vout?

  21. Comparator If Vi>Vr, then Vo=“1” Else zero.

  22. A Simple Op-Amp Based Comparator

  23. A Analog-to-digital Converter (Inverter) (NAND) EOC: End of Conversion A binary output approximately equal to Vx will be when EOC=1

  24. Sampling in Telephone Systems

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