DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 8.7 Rearranged decoder
R
G
B
Y L*
Y
Departure from constant luminance
To avoid the complexity of incorporating two power
functions into a decoder’s electronics, we begin by rearranging
the block diagram, to interchange the “order of
operations” of the matrix and the CRT compensation:
[P] [P -1
2.5
]
0.4
Figure 8.8 Simplified decoder
R
G
B
Y
Upon rearrangement, the two power functions are adjacent.
Since the functions are effectively inverses, the
combination of the two has no effect. Both functions
can be dropped from the decoder:
The decoder now comprises simply the inverse of the
encoder matrix, followed by the 2.5-power function
that is intrinsic to the CRT. Rearranging the decoder
requires that the encoder also be rearranged, so as to
mirror the decoder and achieve correct end-to-end
reproduction of the original RGB tristimulus values:
The rearranged flow diagram of Figure 8.9 is not mathematically
equivalent to the arrangement of Figures 8.1
through 8.4! The encoder’s matrix no longer operates
on (linear) tristimulus signals, and relative luminance is
no longer computed. Instead, a nonlinear quantity Y’,
denoted luma, is computed and transmitted. Luma
involves an engineering approximation: The system no
longer adheres strictly to the Principle of Constant Luminance
(though it is often mistakenly claimed to do so).
78 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES
1 ⁄2.5
[P] [P -1
]
0.4
L*
Figure 8.9 Rearranged encoder
R
G
B
0.4
R’
G’
B’
Y’
Television engineers who are
uneducated in color science often
mistakenly call luma (Y’) by the
name luminance and denote it by
the unprimed symbol Y. This leads
to great confusion, as I explain in
Appendix A, on page 595.
[P] [P -1
]
2.5
2.5
2.5