# hw2 - Due Monday, 10/3/05 at 5 PM ECE 638 1. Homework No. 2...

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Due Monday, 10/3/05 at 5 PM ECE 638 Homework No. 2 Fall 2005 1. Consider a finite dimensional model for a linear, bichromatic vision system. Assume that we sample at N = 3 wavelengths. Suppose that the sensor response matrix is given by S = 1 0 1 1 0 1 a. Find the response of this sensor to the stimulus n = 1 2 3 [ ] T . b. Find the fundamental component n * for this stimulus. c. Find the black-space component n c for the stimulus. d. Find a metamer n to n such that n n . 2. Let S be a 31 × 3 matrix with rank 3; and let S = span( S ) . Let v be any vector S . Show by differentiation with respect to the elements of a that the vector u S that is closest to v in the Euclidean norm is given by u = S a , where a = S T S [ ] 1 S T v . (Note that you should establish that the stationary point is in fact a minimum.) 3. Using the expression R = S S T S ( ) 1 S T , show that the projection operator

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## This note was uploaded on 02/19/2012 for the course ECE 638 taught by Professor Staff during the Fall '08 term at Purdue.

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hw2 - Due Monday, 10/3/05 at 5 PM ECE 638 1. Homework No. 2...

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