| 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) <br> |
<math> | <math> | ||
\left[ {\begin{array}{*{20}{c}} | \left[ {\begin{array}{*{20}{c}} | ||
| Line 23: | Line 23: | ||
F_2\\ | F_2\\ | ||
F_3 | F_3 | ||
| − | \end{array}} \right] = {\begin{array}{*{20}{c}} | + | \end{array}} \right] |
| − | \int_{-\infty}^{infty} | + | = |
| − | + | {\begin{array}{*{20}{c}} | |
| − | \end{array}} \left[ {\begin{array}{*{20}{c}} | + | \int_{-\infty}^{\infty} |
| − | + | \end{array}} | |
| − | + | \left[ {\begin{array}{*{20}{c}} | |
| − | + | f_1(\lambda)\\ | |
| + | f_1(\lambda)\\ | ||
| + | f_1(\lambda) | ||
\end{array}} \right] | \end{array}} \right] | ||
| + | I(\lambda)d\lambda | ||
</math> | </math> | ||
Revision as of 19:57, 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[ {\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}} f_1(\lambda)\\ f_1(\lambda)\\ f_1(\lambda) \end{array}} \right] I(\lambda)d\lambda $
