## Rec. 709 Versus Rec. 601 Luma Coefficients

The Rec. 709 standard (used for most HD formats) specifies different luma coefficients than Rec. 601, which can cause potential problems in consumer equipment. Component signals need conversions between the two color spaces when down/upsampling the image. No conversion would result in color inaccuracies in the green channel of the image.

In much of consumer equipment, there is no matrix to convert between the Rec. 709 and Rec. 601 color spaces as this omission lowers cost. The following images simulate the difference. When Rec. 709 material is decoded with Rec. 601 numbers, the flesh tends tend towards magenta. In the reverse scenario, they tend towards green and appear more yellow.

 Original. Rec. 709 encoded, decoded with Rec. 601 coefficients. Rec. 601 encoded, decoded with Rec. 709 coefficients.

### The Math Simplified

In component encoding, the R'G'B' signal is converted/transformed into Y', B'-Y', and R'-Y components. All you need to know is that using the wrong pairing of formulas will cause errors in the green channel.

Input: R', G', B'

 Y' = 0.299 R' + 0.587 G' + 0.114 B' (Rec. 601 coefficients) OR Y' = 0.2126 R' + 0.7152 G' + 0.0722 B' (Rec. 709 coefficients) B'-Y' = B'-Y' R'-Y' = R'-Y'

To convert back into R'G'B':

 B' = (B'-Y') + Y' R' = (R'-Y') + Y' G' = ( Y' - 0.299 R' - 0.114 B') / 0.587 (Rec. 601 coefficients) OR G' = ( Y' - 0.2126 R' - 0.0722 B') / 0.7152 (Rec. 709 coefficients)

### Nitty Gritty Details

The Rec. 601 and Rec. 709 color spaces also differ in the transfer functions used, and the chromaticities of the primary colors (i.e. in a CRT, the color of the standard red, green, and blue phosphors are different). These other differences are much less significant. In practice, they can be ignored.

The transitional 1035i format uses the same coefficients as Rec. 601.

An excellent resource for the nitty gritty engineering details can be found in Charles Poynton's Digital Video and HDTV (see poynton.com).

This site by Glenn Chan. Please email any comments or questions to glennchan /at/ gmail.com

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