3.4 Colorimetric characteristics of digital television systems

Colorimetric characteristics of standard definition and high definition digital television systems are presented in Table 3.2, where:

– relative luminance levels of -image components;

– gamma-corrected -signals relative levels ( );

, , , – color-difference signals, normalized to the interval .

In Recommendation ITU-R BT.601 [3.4] for digital SDTV systems 8 bit and 10 bit coded representation is used and decimal values of the quantized signals are:

‒ for gamma-corrected signals:

(3.6)

(3.7)

(3.8)

TABLE 3.1 Analogue television systems colorimetric characteristics

System	Primaries and reference white chromaticity coordinates					Opto-electronic and electro-optic conversion characteristics	Coding equation
NTSC (SMPTE 170M 3.2, ITU-R BT.1700 3.3, Part 1)						Opto-electronic conversion: Electro–optic conversion:
			x	y
		Red	0.630	0.340
		Green	0.310	0.595
		Blue	0.155	0.070
		White D65	0.3127	0.3290
PAL 525 lines (ITU-R BT.1700 3.3, Part 2)						Assumed “gamma” value for displaying device is equal to 2.2
			x	y
		Red	0.630	0.340
		Green	0.310	0.595
		Blue	0.155	0.070
		White D65	0.3127	0.3290
PAL 625 lines (ITU-R BT.1700 3.3, Part 2)						Assumed “gamma” value for displaying device is equal to 2.2
			x	y
		Red	0.640	0.330
		Green	0.290	0.600
		Blue	0.150	0.060
		White D65	0.3127	0.3290
SECAM (ITU-R BT.1700 3.3, Part 3)						Assumed “gamma” value for displaying device is equal to 2.2
			x	y
		Red	0.640	0.330
		Green	0.290	0.600
		Blue	0.150	0.060
		White D65	0.3127	0.3290

TABLE 3.2 Colorimetric characteristics of standard definition and high definition digital television systems

System	Primaries and reference white chromaticity coordinates							Opto-electronic and electro–optic conversion characteristics	Coding equation
SDTV 625/50/2:1 (ITU-R BT.601-6 3.4, item 3.6) 525/50/1:1 (ITU-R BT.1358 3.5)								Opto-electronic conversion:
		Red	0.640		0.330
		Green	0.290		0.600
		Blue	0.150		0.060
		White D65	0.3127		0.3290
SDTV 625/60/2:1 (ITU-R BT.601-6 3.4, item 3.6) 525/60/1:1 (ITU-R BT.1358 3.5)								Opto-electronic conversion:
			x		y
		Red	0.630		0.340
		Green	0.310		0.595
		Blue	0155		0.070
		White D65	0.3127		0.3290
HDTV 1125/60/2:1 (ITU-R BT.709 3.6, Part 1)								Opto-electronic conversion:
				x		y
		Red		0.640		0.330
		Green		0.300		0.600
		Blue		0.150		0.060
		White D65		0.3127		0.3290
HDTV 1250/50/2:1 (ITU-R BT.709 3.6, Part 1)								Opto-electronic conversion:
				x		y
		Red		0.640		0.330
		Green		0.300		0.600
		Blue		0.150		0.060
		White D65		0.3127		0.3290

TABLE 3.2 (End)

System	Primaries and reference white chromaticity coordinates					Opto-electronic and electro–optic conversion characteristics	Coding equation
HDTV with square active pixels (ITU-R BT.709 3.6, Part 2						Opto-electronic conversion:
			x	y
		Red	0.640	0.330
		Green	0.300	0.600
		Blue	0.150	0.060
		White D65	0.3127	0.3290
720p (ITU-R BT.1543 3.7, ITU-R BT.1847 3.8)						Opto-electronic conversion:
			x	y
		Red	0.640	0.330
		Green	0.300	0.600
		Blue	0.150	0.060
		White D65	0.3127	0.3290
Unified colorimetry (ITU-R BT.1361 3.9)						Opto-electronic conversion: Note. Conversion for corresponds to systems with extended color gamut.
			x	y
		Red	0.640	0.330
		Green	0.300	0.600
		Blue	0.150	0.060
		White D65	0.3127	0.3290

‒ for luminance and colour difference signals:

(3.9)

(3.10)

(3.11)

where D takes either the value 1 or 4, corresponding to 8 bit and 10 bit quantization respectively. The operator int ( ) returns the value of 0 for fractional parts in the range of 0 to 0.4999 … and +1 for fractional parts in the range 0.5 to 0.999 ..., i.e. it rounds up fractions above 0.5.

Equations for derivation quantized luminance and color-difference signals via quantized gamma-corrected signals are

(3.12)

(3.13)

(3.14)

where k′ and m denote the integer coefficients and the bit-lengths of the integer coefficients, respectively k′ coefficients are presented in Table 3.3.

TABLE 3.3 Optimized integer coefficients for SDTV systems (Recommendation ITU-R BT.601)

Coeff. Bits	Denominator	Luminance Y			Color-difference CR			Color-difference CB
m		k’Y1	k’Y2	k’Y3	k’CR1	k’CR2	k’CR3	k’CB1	k’CB2	k’CB3
8	256	77	150	29	131	-110	-21	-44	-87	131
9	512	153	301	58	262	-219	-43	-88	-174	262
10	1024	306	601	117	524	-439	-85	-177	-347	524
11	2048	612	1202	234	1047	-877	-170	-353	-694	1047
12	4096	1225	2404	467	2095	-1754	-341	-707	-1388	2095
13	8192	2449	4809	934	4189	-3508	-681	-1414	-2776	4190
14	16384	4899	9617	1868	8379	-7016	-1363	-2828	-5551	8379
15	32768	9798	19235	3735	16758	-14033	-2725	-5655	-11103	16758
16	65536	19595	38470	7471	33516	-28066	-5450	-11311	-22205	33516

The same digital coding in Recommendation ITU-R BT.1358 [3.5] is defined for SDTV systems with progressive scanning.

In Recommendations ITU-R BT.709 [3.6], ITU-R BT.1543 [3.7] and ITU-R BT.1847 [3.8] for digital HDTV systems 8 bit and 10 bit coded representation is used and decimal values of the quantized signals are:

‒ for gamma-corrected signals:

(3.15)

(3.16)

(3.17)

‒ for luminance and colour difference signals:

(3.18)

(3.19)

(3.20)

where n denotes the number of the bit length of the quantized signal.

Derivation of luminance and colour-difference signals via quantized RGB signals is realised using equations:

(3.21)

(3.22)

(3.23)

Colorimetric parameters and related characteristics to be used for future television and imaging systems with conventional and extended (based on use negative values of signals) colorimetry compatible with Recommendation ITU-R BT.709 [3.6] are specified in Recommendation ITU-R BT.1361 [3.9]. In Table 3.4 equations for quantization of RGB luma and chroma signals and equations for derivation of luma and chroma signals via quantized RGB signals are presented. In the following, m and n denote the bit-lengths of the integer coefficients and digital signals, respectively.

In the case of derivation of luminance and color-difference signals via quantized RGB signals digital luminance and color-difference signals may take slightly different values depending on the signal processing sequence, i.e. the discrepancy between signals quantized after analogue matrixing and signals digitally matrixed after quantization of RGB signals.

In Recommendation ITU-R BT.1361 [3.9] following equations with optimized coefficients are derived:

• for conventional color gamut system:

(3.24)

(3.25)

(3.26)

where coefficients are presented in Table 3.5;

• for extended color gamut system:

(3.27)

(3.28)

(3.29)

where coefficients are presented in Table 3.6.