{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 5

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

This preview shows pages 1–6. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 22

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online