| Line 17: | Line 17: | ||
b) The CIE color matching functions are not always positive. <math> r_0(\lambda) </math> takes negative values. This is the case because, to match some reference color that is too saturated, colors have to be subtracted from the <math> R, G, </math> and <math> B</math> primaries. This results in negative values in tristimulus values r, g, and b. So the color matching functions at the corresponding wavelength have negative values. | b) The CIE color matching functions are not always positive. <math> r_0(\lambda) </math> takes negative values. This is the case because, to match some reference color that is too saturated, colors have to be subtracted from the <math> R, G, </math> and <math> B</math> primaries. This results in negative values in tristimulus values r, g, and b. So the color matching functions at the corresponding wavelength have negative values. | ||
| − | c) | + | c) <math> \left</math> |
| + | <math> | ||
| + | \left[ {\begin{array}{*{20}{c}} | ||
| + | F_1\\ | ||
| + | F_2\\ | ||
| + | F_3 | ||
| + | \end{array}} \right] = {\begin{array}{*{20}{c}} | ||
| + | \int_{-\infty}^{infty} | ||
| + | |||
| + | \end{array}} \left[ {\begin{array}{*{20}{c}} | ||
| + | r_0(\lambda)\\ | ||
| + | g_0(\lambda)\\ | ||
| + | b_0(\lambda) | ||
| + | \end{array}} \right] | ||
| + | </math> | ||
Revision as of 19:55, 10 November 2014
ECE Ph.D. Qualifying Exam in Communication Networks Signal and Image processing (CS)
Question 5, August 2013, Part 2
part1, part 2
Solution 1:
a) If the color matching functions $ f_k(\lambda) $ has negative values, it will result in negative values in $ F_k $. In this case, the color can not be reproduced by this device.
b) The CIE color matching functions are not always positive. $ r_0(\lambda) $ takes negative values. This is the case because, to match some reference color that is too saturated, colors have to be subtracted from the $ R, G, $ and $ B $ primaries. This results in negative values in tristimulus values r, g, and b. So the color matching functions at the corresponding wavelength have negative values.
c) $ \left $ $ \left[ {\begin{array}{*{20}{c}} F_1\\ F_2\\ F_3 \end{array}} \right] = {\begin{array}{*{20}{c}} \int_{-\infty}^{infty} \end{array}} \left[ {\begin{array}{*{20}{c}} r_0(\lambda)\\ g_0(\lambda)\\ b_0(\lambda) \end{array}} \right] $
