From Continuous Time System to Discrete Time System ES400 Jack Ou, Ph.D. Chapter 1
Dec 17, 2015
From Continuous Time System to Discrete Time System
ES400Jack Ou, Ph.D.
Chapter 1
Outline
• Modeling –Signal–System
• Continuous Time System• ADC• Discrete Time System
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.
Example of a Continuous Time Signal
Criterion: The signal defined for all values of timeTechniques: Fourier series, Fourier transform, Laplace transform
Example of a Discrete Time Signal
Criterion: The signal is defined for at only certain instants of time Technique: Z transform, DFT, FFT
Tinkering
Mathematical Modeling of a Physical System
Mathematical Solutions of Physical Problems
1. Formulate a math model for physical signal and system involved.2. Equations are solved for typical excitation function. 3. Compare math solution with the response of the physical system4. Iterate the process until close correlation between the measuredand model is achieved.
Continuous Time Example
Mathematical Modeling of Elementary Circuits
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.
Describe the input signal mathematically
Represent Input Voltage Source using Laplace Transform
Solve the problem in the Laplace Domain
• Laplace transform the KVL expression
• Solve the variable of interest• Inverse Laplace Transform
Not All Systems Can Be Represented Using a Continuous Time Representation
Convert a Signal From Continuous Time System to Discrete Time System
• Operational Amplifier• Digital to Analog Converter• Comparator• Counter-Ramp Analog to Digital
Converter
Operational Amplifier
If used in a feedback configuration, V+=V-.
Large input impedance!
A Simple Voltage Amplifier
Digital-to-analog Converter
Purpose: Convert a binary number to a voltage.
A Simple Digital to Analog Converter
Assume “1”=5V, “0”=0VD0=“1”, D1=“0”, D2=“0”What is Vout?
Comparator
If Vi>Vr, then Vo=“1”Else zero.
A Simple Op-Amp Based Comparator
A Analog-to-digital Converter
(Inverter)
(NAND)
EOC: End of ConversionA binary output approximately equal to Vx will be when EOC=1
Sampling in Telephone Systems