Lecture 3

# Lecture 3 - ECE 3101 Signals and Systems Reading Assignment Sects 1.6-1.8-1 1.9 1.10 10.1-10.2-1 Problem Set 1 Due Thursday Last Time 1.4 Some

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Lecture 3, 1/27/11 ECE 3101, Copyright P. B. Luh 1 Reading Assignment: Sects. 1.6-1.8-1, 1.9, 1.10, 10.1-10.2-1 Problem Set 1: Due Thursday Last Time: 1.4 Some Useful Signal Models Elementary Signals: Step, Ramp, and Sign Functions/Sequences Trigonometric Functions and Sequences Complex Functions and Sequences Unit Impulse Function and Unit Impulse Sequence 1.5 Even and Odd Functions and Sequences ECE 3101 Signals and Systems

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Lecture 3, 1/27/11 ECE 3101, Copyright P. B. Luh 2 Today: Systems 1.6 Systems 1.7 Classification of Systems: RLC Circuits with Input- Output Description Liner vs. nonlinear; Time invariant vs. time varying Additional system properties: Instantaneous vs. dynamic; Causal vs. non-causal; Finite dimensional vs. infinite dim. 1.10 and 10.1, 10.2 State-Space Description Next Time: Sections 1.8-2 to 1.11 1.8 System Modeling: Integrators/Differentiators, Op-Amps, and Mechanical Systems 3.4 and 3.5 Discrete-Time Systems
Lecture 3, 1/27/11 ECE 3101, Copyright P. B. Luh 3 Broadly speaking, a system is anything that responds when stimulated or excited Systems accept excitations or input signals at their inputs and produce responses or output signals at their outputs The above is a single-input single-output system 1.6 Systems u( t )

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Lecture 3, 1/27/11 ECE 3101, Copyright P. B. Luh 4 A multiple-input multiple-output system u 1 ( t ) u 2 ( t ) We have seen several examples of systems in Lecture 1
Lecture 3, 1/27/11 ECE 3101, Copyright P. B. Luh 5 What are the key system characteristics? Using, for example, a savings account in a bank With a fixed interest rate. A linear and time-invariant system Interest rate is time varying. A time varying system Interest rate depends on the amount of money in the account. A nonlinear system Future interest rates are uncertain. An uncertain system Depending on the characteristics System properties could be quite different Methods of analysis and synthesis could be quite different We shall study system classification next

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6 1.7 Classification of Systems: RLC Circuits Elements: R, L, C, and voltage and current sources How to describe these elements? The systems? + + - - - u(t) R C L + y R v - + i v = Ri L v - + i dt di L v = C v - + i dt dv C i = Linearity i 1 v 1 = R i 1 2i 1 2v 1 ; Homogeneity i 2 v 2 = R i 2 i 1 + i 2 v 1 + v 2 ; Additivity u 1 y 1 2 y 2 , then k 1 u 1 + k 2 u 2 k 1 y 1 + k 2 y 2 ; Linearity Are R, L, and C linear elements? Yes. Differentiation is a linear operation
Lecture 3, 1/27/11 ECE 3101, Copyright P. B. Luh 7 i v Linearity: A straight line passing through the origin Time-invariance: The characteristics of an element do not change over time v = Ri ~ Linear time-invariant element v = R(t) i ~ Linear time-varying element Similar v = L di/dt ( LTI ) vs. v = L(t) di/dt ( LTV ) u(t) y(t), then u(t-t 1 ) y(t-t

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## This note was uploaded on 03/29/2011 for the course ECE 3101 taught by Professor Luh during the Spring '11 term at UConn.

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Lecture 3 - ECE 3101 Signals and Systems Reading Assignment Sects 1.6-1.8-1 1.9 1.10 10.1-10.2-1 Problem Set 1 Due Thursday Last Time 1.4 Some

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