ECE 638 Exam No. 1 Fall 2013

4 October 2013 ECE 638 Exam No. 1 ECE 638 Exam No. 1 Fall 2013

This exam is closed book and closed notes. You have 50 minutes to work the following three problems. To obtain maximum partial credit, be sure to show the complete derivation of your answers.

1. (40 pts.) Consider a three-channel sensor with the response functions shown below.

a. (8) Find the response of this sensor to the stimulus with the spectral power distribution shown below:

b. (8) Carefully sketch the sensor chromaticity diagram for this sensor. Consider the primary set with power spectral distribution shown below:

c. (8) Find the amounts of each of the three primaries that will yield a match to the stimulus from part a), as viewed by the sensor with response functions shown above. d. (8) Find the color matching functions for this primary set. e. (8) Use the color matching functions as an alternate solution to finding the amounts of the primaries that will match the stimulus shown above.

1. (continued - 1) 4 October 2013 ECE 638 Exam No. 1 1. (continued - 2) 4 October 2013 ECE 638 Exam No. 1

2. (25 pts.) Consider a finite dimensional model for a linear, bichromatic (2-channel) vision system. Assume that we sample at wavelengths. Suppose that the sensor response matrix is given by

a. (5) Find the response of this sensor to the stimulus .

b. (5) Find the fundamental component for this stimulus.

c. (5) Find the black-space component for the stimulus.

d. (5) Find a metamer to such that .

e. (5) Find the projection operator for this sensor. 4 October 2013 ECE 638 Exam No. 1

2. (continued)

3. (35 pts.) Consider the 2-D signal shown below 4 October 2013 ECE 638 Exam No. 1

a. (7) Find a closed-form expression for that does not contain any operators.

b. (7) Find a closed-form expression for the 2-D Continuous-Space Fourier Transform (CSFT) of that does not contain any operators.

c. (7) Carefully sketch a fully dimensioned plot for .

Define a new signal that is equal to from part a) above within the region , and is equal to 0 elsewhere.

d. (7) Find a closed-form expression for the 2-D Continuous-Space Fourier Transform (CSFT) of that does not contain any operators.

e. (7) Carefully sketch a fully dimensioned plot for . 4 October 2013 ECE 638 Exam No. 1

3. (continued - 1) 4 October 2013 ECE 638 Exam No. 1

3. (continued - 2) 4 October 2013 ECE 638 Exam No. 1 3. (continued - 3) 4 October 2013 ECE 638 Exam No. 1

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