Lecture 4

# Lecture 4 - ECE 3101 Signals and Systems Makeup classes...

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Lecture 4, 2/8/11 ECE 3101, Copyright P. B. Luh 1 Makeup classes Thursday, 2/10/11, 6:15-7:30 pm, MSB 403 Monday, 2/21/11, 6:15-7:30 pm, MSB 411 Wednesday, 3/2/11, 6:15-7:30 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: Next Monday during discussion session. One problem. Covering to the end of last Thursday’s lecture Examine 1: Thursday next week 2/17/11 in class. Four problems. Covering to the end of today’s lecture Additional Office Hours: Friday 2/11/11, 10-11 am (tentative); Monday 2/14/11, 11-12:30 ECE 3101 Signals and Systems

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Lecture 4, 2/8/11 ECE 3101, Copyright P. B. Luh 2 Reading Assignment: Sections 1.8-1.11, 3.4 Problem Set 2: Due next Tuesday. 1.7.-1 (b, d, f, h), 1.7-2 (b, d, f), 1.7-11 (b, c, d, e), 1.8-3, 1.8-5, 1.10-2 Last Time: Systems Classification of Systems: RLC Circuits with I/O Description Linearity: u 1 y 1 and u 2 y 2 , then k 1 u 1 + k 2 u 2 k 1 y 1 + k 2 y 2 Time invariance: u(t) y(t), then u(t-t 1 ) u(t-t 1 ) for all t 1 An LTI system is described by linear differential equations with constant coefficients Additional System Concepts: ECE 3101 Signals and Systems
Lecture 4, 2/8/11 ECE 3101, Copyright P. B. Luh 3 Causality: y(t) does not depend on future input Instantaneous: y(t) depends on u(t) only Dimensionality: Number of initial conditions needed State-Space Description: x' = Ax + Bu, and y = Cx + Du Today: System Modeling: Integrators and Differentiators Circuits with Op-Amps Mechanical Systems Discrete-time systems Next Time: Time Domain Analysis of C-T Systems, 2.1-2.3

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Integrators and Differentiator Elements: Multipliers, differentiators, and integrators Differentiator u(t) y(t) = du/dt S Multiplier u(t) y(t) = au(t) a Integrator u(t) y(t) = 1/S ) t ( y d ) ( u 0 t t 0 + τ τ = τ Are they LTI elements? Yes Which one has memory? What are their dimensions? Integrator has memory Dimensions: 0, 0, and 1 Interconnection of these elements to form LTI systems
Lecture 4, 2/8/11 ECE 3101, Copyright P. B. Luh 5 2 1/s 1/s - u(t) y(t) τ τ = d ) ( y 2 u y u y 2 y + = y τ τ d ) ( y Input/output equations? A second order linear differential equation with constant coefficients State and output equations?

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Lecture 4, 2/8/11 ECE 3101, Copyright P. B. Luh 6 How many state variables? Which ones? Number of state variables = number of integrators Output of integrators 2 1/s 1/s + - u(t) y(t) x 1 x 2 2 1 x x = 1 2 x 2 u x = y = x 2 u 1 0 x x 0 2 1 0 x x 2 1 2 1 + = [] u 0 x x 1 0 y 2 1 + = A B C D Linear differential equations with constant coefficients Again, x' = Ax + Bu, and y = Cx + Du In matrix form?
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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 4 - ECE 3101 Signals and Systems Makeup classes...

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