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Unformatted text preview: Section 3.3 24 Find the best straightline fit to the following measurements, and sketch your solution: y = 2 at t = 1 , y = 0 at t = 0 , y = 3 at t = 1 , y = 5 at t = 2 . Solution. Suppose the line is given by y = u + v · t. To determine u and v , we need to solve the system u + v · ( 1) = 2 u + v · = u + v · 1 = 3 u + v · 2 = 5 , that is, 1 1 1 1 1 1 2 " u v # = 2 3 5 , which is obviously inconsistent. The best solution given by the least squares method is " ˆ u ˆ v # = ( A T A ) 1 A T b = " 3 / 10 12 / 5 # . 25 Suppose that instead of a straight line, we fit the data in Problem 24 by a parabola: y = C + Dt + Et 2 . In the inconsistent system Ax = b that comes from the four measurements, what are the coefficient matrix A , the unknown vector x , and the data vector b ? You need not compute ˆ x ....
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This note was uploaded on 01/14/2011 for the course EECS 551 taught by Professor Wakefield during the Spring '08 term at University of Michigan.
 Spring '08
 Wakefield
 Signal Processing

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