ECE3101S11Lec10

# ECE3101S11Lec10 - ECE 3101 Signals and Systems Reading...

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Lecture 10, 2/24/11 ECE 3101, Copyright P. B. Luh 1 ECE 3101 Signals and Systems Reading Assignment: Sections 4.1 and 4.2 Problem Set 4: Due next Tuesday The class on Tue. 3/1/11 and the discuss session on Mon. 3/14/11 will be swapped Quiz 2, Tuesday 3/1, end of Ch. 2, 1 problem, 4 cheat sheets See problems in SampleECE3101Exam1 and SampleECE3101Exam1a The last makeup class: Wed., 3/2/11, 6:30 pm, MSB 411

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Lecture 10, 2/24/11 ECE 3101, Copyright P. B. Luh 2 Last Time: Unit Impulse Response • y[k+N] + a 1 y[k+N-1] + … + a N-1 y[k+1] + a N y[k] = b 0 u[k+N] + b 1 u[k+N-1] + … + b N-1 u[k+1] + b N u[k] h[k] = (b N /a N ) δ [k] + y c [k]U[k] , to match h[0], h[1], . ., h[N-1] h[k] = A 0 δ [k] + A 1 δ [k-1] + y c [k]U[k] if a N = 0 Zero State Resp: h[k] u[k] Σ m h[k-m]u[m] = Σ m h[m]u[k- m] Convolution of Discrete-Time Signals Direct sum from definition • The Semi-Graphical Method: f[k] g[k] = Σ m f[m] g[k-m] Properties of Convolution: Commutative, Associative, Distributive, Shifting, Convolution with δ [k], Step Response, and the Width Property
3 Today Frequency Domain Analysis of Continuous-Time LTI Systems: Laplace Transform ~ STAY ON TOP!! Converting linear differential equations with constant coefficients into algebraic equations that can be easily solved The Definition of Laplace Transform Properties of the Laplace Transform Next Time: Sections 4.2 and 4.3

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Lecture 10, 2/24/11 ECE 3101, Copyright P. B. Luh 4 4. Transform Domain Analysis by Laplace Transform 4.1 Laplace Transform for LTIC Systems From Chapter 1, a continuous-time LTI system can be described by y (N) + a 1 y (N-1) + . . + a N-1 y (1) + a N y = b 0 u (N) + b 1 u (N-1) + . . + b N-1 u (1) + b N u x (1) = Ax + Bu, and y = Cx + Du Linear differential equations with constant coefficients How to solve them? Although we love convolution, however, … Simpler way? Laplace transform: Converting linear differential equations with constant coefficients into algebraic equations that can be easily solved
Lecture 10, 2/24/11 ECE 3101, Copyright P. B. Luh 5 We shall study The definition of Laplace transform Why it works Properties of Laplace transform Inverse Laplace transform Using Laplace transform to solve I/O equations and state and output equations Differential equations in terms of x or y Algebraic equations in terms of X or Y Solution to algebraic equations in terms of X or Y Solution to differential equations in terms of x or y Laplace Transform Inverse Laplace Transform Difficult convolution

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Lecture 10, 2/24/11 ECE 3101, Copyright P. B. Luh
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ECE3101S11Lec10 - ECE 3101 Signals and Systems Reading...

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