Lecture 1

Lecture 1 - ECE 3101 Signals and Systems Am I in the right...

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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 1 ECE 3101 Signals and Systems Instructor: Peter B. Luh ITEB 348, P: 486-4821, F: 486-5585, E: [email protected] Tue. 11:00-12:30, Thur. 2:00-3:30, or by appointment Teaching Assistant: Manisha Mishra BECAT Room A24, P: 486- 5965 , E: [email protected] Wed. 9:00-10:3:00, Fri. 2:00-3:30, ITEB 430 , or by appointment Am I in the right classroom ?
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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 2 Reading Assignment: B.1-B.7 (except B.5), 1.1-1.3 Today: 1.0 Introduction Motivating Examples Basic Classification of Signals Course Overview 1.1 Size of a Signal 1.2 Some Useful Signal Operations 1.3 Classification of Signals: Periodic and Aperiodic Signals Next Time: 1.4-1.5 1.4 Some Useful Signal Models 1.5 Even and Odd Functions
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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 3 1.0 INTRODUCTION Motivating Examples Example 1. How to model the reproduction of rabbits? Initially one young pair Takes one month to mature and then produces one pair per month. Same for others They never die How many pairs at month 5? 1 How to mathematically model this process?
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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 4 1.0 INTRODUCTION Motivating Examples Example 1. How to model the reproduction of rabbits? Initially one young pair Takes one month to mature and then produces one pair per month. Same for others They never die How many pairs at month 5? 1 How to mathematically model this process?
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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 5 The model: f[n+2] = f[n] + f[n+1] for k 0, with f[1] = 1 and f[2] = 1 A difference equation . What are the signals? What is f[3]? f[4]? f[5]? f[3] = 1 + 1 = 2 f[4] = 1 + 2 = 3 f[5] = 2 + 3 = 5 The Fibonacci sequence. What is f[12]? f[12] = 144 What is f[10,000]? How to efficiently compute f[n] for an arbitrary n?
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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 6 Example 2. Want to buy a new car? A $16,000 car loan is to be retired in 4 years by equal monthly payment with interest 1% per month on the unpaid balance What is the monthly payment u? How about and the balance at end of month n, y[n]? What is y[0]? What is y[48]? y[0] = 16,000, y[48] = 0 How to describe the relationship between y[n+1] and y[n]? y[n+1] = y[n] + 0.01y[n] - u A difference equation . What are the signals? What is u? y[1]? y[2]? y[3]? or y[n] for an arbitrary n?
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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 7 Example 3. Do you want to become a millionaire in 20 years? Suppose that you deposit an equal amount of money at the beginning of a month with interest 1% per month without withdrawal Want to compute the monthly deposit u and the balance at month n, y[n] What is y[0]? What is y[240]? y[0] = u, y[240] = 1,000,000 How to describe the relationship between y[n+1] and y[n]? y[n+1] = y[n] + 0.01y[n] + u What is u? y[1]? y[2]? y[3]? or y[n] for an arbitrary n?
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Lecture 1, 1/18/11 ECE 3101, Copyright P. B. Luh 8 Example 4. How to model a warfare?
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Lecture 1 - ECE 3101 Signals and Systems Am I in the right...

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