Lecture 5

Lecture 5 - ECE 3101 Signals and Systems Reading...

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Lecture 5, 2/10/11 ECE 3101, Copyright P. B. Luh 1 Reading Assignment: Sec. 2.1-2.3, 2.8 Problem Set 2: Due next Tuesday in class. No late homework Additional Office Hours: Friday 2/11/11, 11:30-12:30; Monday 2/14/11, 11-12:30 Makeup classes Tonight, 2/10/11, 6:30-7:45 pm, MSB 403 Monday, 2/21/11, 6:30-7:45 pm, MSB 411 Wednesday, 3/2/11, 6:30-7:45 pm, MSB 411 Also, I will be at NSF on Tue. 3/1/11. Makeup class: Mon. 3/14/11 during discussion session (after Spring break) Quiz 1: Monday. One problem. To the end of Lecture 4. Two cheat sheets ECE 3101 Signals and Systems
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Lecture 5, 2/10/11 ECE 3101, Copyright P. B. Luh 2 Examine 1: Thursday next week 2/17/11 in class. Four problems. To the end of Chapter 1. Four cheat sheets Last Time: State and Output Equations State: A set of variables which along with future input is sufficient to determine the future behavior of the system State variables for circuits: {i L , v C } Generic form: x' = Ax + Bu, y = Cx + Du System Modeling Integrator/Differentiator Realizations: x ~ Output of integrators Circuits with Op-Amps: i a = i b = 0 and v a = v b Modeling of Mechanical Systems Determine ALL junctions, and draw free body diagrams Apply Newton's law of motion to each free body diagram
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Lecture 5, 2/10/11 ECE 3101, Copyright P. B. Luh 3 Discrete-time systems Choose outputs of delay elements as state variables Go to the inputs of delay elements, and obtain x[n+1] in terms of x[n] and u[n] Today Time-Domain Analysis of Continuous-Time Systems Introduction: y(t) = y ZI (t) + y ZS (t) for linear systems Zero Input Response: Characteristic polynomial and characteristic modes Unit Impulse Response Next Time: 2.4 Zero State Response
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4 Given u(t) to find y(t). Two approaches will be examined: Time domain analysis of input/output descriptions Response caused by initial conditions: Zero input response Based on characteristic polynomial Response caused by input: Zero state response Based on linearity, time invariance, and response to δ (t) ( unit impulse response ) Total response: y(t) = y ZI (t) + y ZS (t) ~ Based on linearity Transform domain analysis: Laplace transform (later) Converting linear differential equations with constant coefficients into algebraic equations Input/Output description State variable description 2. Time Domain Analysis of C-T LTI Systems
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5 Zero Input Response Example: y'' + 5y' + 6y = 0, with y 0 (0) = 1, y 0 '(0) = 1. y 0 (t) = ? (D 2 + 5D + 6)y 0 = 0 What is the general form of solution for LTI systems ? How about a polynomial, e.g., y 0 (t) = c t 6 ? y 0 '(t) = 6c t 5 , y 0 ''(t) = 30c t 4 , y 0 '' + 5y 0 ' + 6 y 0 = ct 4 (30 + 6t + t 2 ) To satisfy (D 2 + 5D + 6)y 0 = 0, c = 0, and y 0 (t) 0. No good How about an exponential function, e.g., y 0 (t) = c e λ t , with λ yet to be determined?
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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 5 - ECE 3101 Signals and Systems Reading...

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