Chapter 5 Week 6 EE 341 Clark Lecture Notes - 6 may

Chapter 5 Week 6 EE 341 Clark Lecture Notes - 6 may - EE...

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EE 341 Discrete-Time Linear Systems – Week 6 Spring 2011 Page 1 Text reading assignment for this week: Chapter 5, Sec 0 – 5. Reminder: Your Midterm Exam will be held on Tuesday, May 3rd at 9:30-10:20 in EE 125. It will cover all lecture, homework, lab, and textbook material covered thru May 3rd. The test is open notes and open book. Outline of this course, so far: Chapters 1: Applications, discrete-time signals, time-shifts, time-scaling, and DT system properties (2 weeks). Chapter 2: Discrete-time convolution, DT linear time-invariant (LTI) systems and difference equations (1 week). Chapter 3: The discrete-time Fourier series and the closely-related discrete Fourier transform (DFT) (2 weeks).
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EE 341 Discrete-Time Linear Systems – Week 6 Spring 2011 Page 2 Example Problem 1 For each of the two cases below, find the convolution [] [] [] yn xn hn . (As always, [] un is the unit step function.) a)  1 2 [] [] 2[ 1 ] n x nn n u n   ,   1 2 n hn b) [] x u n , [] [] [ ] un N 
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EE 341 Discrete-Time Linear Systems – Week 6 Spring 2011 Page 3 Example Problem 2 A system is defined by the difference equation [] [ 5 ] [] yn xn  where, as usual, [] x n is the input and [] is the output. With the assumption that the output signal is zero for 0 n the impulse response of this system is found to be. 0 (1 ) [ 5] k k hn n k  a) Determine the mathematical expression for the output sequence y [ n ] when the input to this system is the two-point pulse signal, [] [] [ 1 ] n n . (Your answer needn’t be in closed f o r m . ) b) Plot y [ n ] below, with enough of a range in n to suggest what it could do for all values of n .
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Chapter 5 Week 6 EE 341 Clark Lecture Notes - 6 may - EE...

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