S08.hw01 - ECE 320 Networks and Systems Spring 20072008...

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ECE 320 Networks and Systems Spring 2007–2008 Problem Set 1 Due January 31, 2008 The section meetings will consider Problems 7, 8, and 9 in detail. 1. Please answer the following questions: (a) Have you already taken ECE 310 “Introduction to Probability and Random Signals”? (b) Are you concurrently taking ECE 310 “Introduction to Probability and Random Signals”? 2. Exercise 2.2 in Professor Fine’s Spring 2008 notes. 3. Exercise 2.3 in Professor Fine’s Spring 2008 notes. 4. Exercise 2.4 in Professor Fine’s Spring 2008 notes. Hint: look carefully at the lower limit in the summation. 5. Exercise 2.8 in Professor Fine’s Spring 2008 notes. 6. Exercise 2.14 in Professor Fine’s Spring 2008 notes. 7. The sole purpose of this problem is to get everyone thinking about Matlab. Consider the following differential equation and initial condition: τ d y d t + y ( t ) = 0 (1) y (0) = y 0 . (2) (a) What is the solution of this differential equation and initial condition? (b) Write a Matlab function that can solve this differential equation for arbitrary values of τ and y 0 , which are inputs to the function. Use a Matlab function like ode45 . Do not use any exponential functions! Please submit a copy of your Matlab code.
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