HW 1 ans - [email protected] icl.syr.edu ELE231 Electrical...

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[email protected] - icl.syr.edu ELE231 - Electrical Fundamentals II - 18JAN2008 Homework Assignment 1 - Due: Friday, 25JAN2008 Problem 1 : The task here is to find a representation for the time signal f(t) in terms of the four basis signals f 1 (t), f 2 (t), f 2 (t), and f 4 (t). That is, find the coefficients c 1 , c 2 , c 3 , and c 4 so that the error term e(t) in the expression below in minimized: f(t) = c 1 f 1 (t) + c 2 f 2 (t) + c 3 f 3 (t) + c 4 f 4 (t) + e(t) (a) Describe what it means to say that the four basis functions shown are orthogonal. Ans: f i (t) f j (t) = 0 when i j . (b) What is the value of the inner product f N (t) f N (t) for each of the basis signals ? Ans: f N (t) f N (t) = 4 for N = 1,2,3, and 4 . (c) Find values for each of the coefficients c 1 , c 2 , c 3 , and c 4 . Ans: c 1 = f(t) f 1 (t) 4 = 4 4 = 1 . c 2 = f(t) f 2 (t) 4 = 1 3 4 = 0 . 5 c 3 = f(t) f 3 (t) 4 = 0 . 25 2 + 1 . 75 4 = 0 . c 4 = 0 . 25 0 . 75 + 1 . 25 1 . 5 4
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This note was uploaded on 05/02/2008 for the course ELE 232 taught by Professor Phelps during the Spring '08 term at Syracuse.

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HW 1 ans - [email protected] icl.syr.edu ELE231 Electrical...

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