# Rec. 709

Diagram of the CIE 1931 color space that shows the Rec. 709 (HDTV) color space in the triangle and the location of the primary colors. Rec. 709 uses Illuminant D65 for the white point.

ITU-R Recommendation BT.709, more commonly known by the abbreviations Rec. 709 or BT.709, standardizes the format of high-definition television, having 16:9 (widescreen) aspect ratio. The first edition of the standard was approved in 1990.

## Technical details

### Pixel count

Rec. 709 refers to HDTV systems having roughly two million luma samples per frame. Rec. 709 has two parts: Part 1 codifies what are now referred to as 1035i30 and 1152i25 HDTV systems. The 1035i30 system is now obsolete, having been superseded by 1080i and 1080p square-sampled ("square-pixel") systems. The 1152i25 system was used for experimental equipment in Europe and was never commercially deployed.

Part 2 codifies current and prospective 1080i and 1080p systems with square sampling. In an attempt to unify 1080-line HDTV standards, part 2 defines a common image format (CIF) with picture parameters independent of the picture rate.

### Frame rate

Rec. 709 specifies the following picture rates: 60 Hz, 50 Hz, 30 Hz, 25 Hz and 24 Hz. "Fractional" rates having the above values divided by 1.001 are also permitted.

Initial acquisition is possible in either progressive or interlaced form. Video captured as progressive can be transported with either progressive transport or progressive segmented frame (PsF) transport. Video captured as interlaced can be transported with interlace transport. In cases where a progressive captured image is transported as a segmented frame, segment/field frequency must be twice the frame rate.

In practice, the above requirements result in the following frame rates ("fractional" rates are specified in commonly used "decimal" form): 25i, 25PsF, 25p, 50p for 50 Hz systems; 23.976p, 23.976PsF, 24p, 24PsF, 29.97i, 29.97p, 29.97PsF, 30PsF, 30p, 59.94p, 60p for 60 Hz systems.

### Digital representation

Rec. 709 coding uses SMPTE reference levels (a.k.a. "studio-swing", legal-range, narrow-range) levels where reference black is defined as 8-bit interface code 16 and reference white is defined as 8-bit interface code 235. Interface codes 0 and 255 are used for synchronization, and are prohibited from video data. Eight-bit codes between 1 and 15 provide footroom, and can be used to accommodate transient signal content such as filter undershoots. Eight-bit interface codes 236 through 254 provide headroom, and can be used to accommodate transient signal content such as filter overshoots. In some camera systems, headroom in the signal is used to contain specular highlights, however, these "extended-range" signals are not allowed in the broadcast system and are clamped during final mastering. Bit-depths deeper than 8 bits are obtained by appending least-significant bits. Ten-bit systems are commonplace in studios. (Desktop computer graphic systems ordinarily use full bit-depth encoding that places reference black at code 0 and reference white at code 255, and provide no footroom or headroom.) The 16..235 limits (for luma; 16..240 for chroma) originated with ITU Rec. 601.[1]

### Primary chromaticities

RGB color space parameters[2]
Color space White point Primaries
xW yW xR yR xG yG xB yB
ITU-R BT.709 0.3127 0.3290 0.64 0.33 0.30 0.60 0.15 0.06

Note that red and blue are the same as the EBU Tech 3213 primaries while green is halfway between EBU Tech 3213 and SMPTE C (two types of Rec.601). In coverage of the CIE 1931 color space the Rec. 709 color space is almost identical to Rec. 601 and covers 35.9%.[3]

#### Standards Conversion

When converting between the various HD and SD formats, it would be correct to compensate for the differences in the primaries (e.g. between the Rec. 709, EBU Tech 3213, and SMPTE C primaries). In practice, this conversion is rarely performed and such a conversion would create a liability for post production facilities as they would need to ensure that the color bars on all the new masters are redone. Correcting for differences in the primaries would cause the resulting color bars on the converted tape to be inaccurate. Incorrect color bars will cause a (sub)master to be rejected by quality control checks.[4]

### Luma coefficients

HDTV according to Rec. 709 forms luma (Y’) using R’G’B’ coefficients 0.2126, 0.7152, and 0.0722. This means that unlike Rec. 601, the coefficients match the primaries and white points, so luma corresponds more closely to luminance. Some experts feel that the advantages of correct matrix coefficients do not justify the change from Rec. 601 coefficients.[5] Although worldwide agreement on a single R’G’B’ system was achieved upon the adoption of Rec. 709, adoption of different luma coefficients created a second flavour of Y’CBCR.

### Transfer characteristics

Rec. 709 is written as if it specifies the capture and transfer characteristics of HDTV encoding - that is, as if it were scene-referred. However, in practice it is output (display) referred with the convention of a 2.4-power function display [2.35 power function in EBU recommendations]. (Rec. 709 and sRGB share the same primary chromaticities and white point chromaticity; however, sRGB is explicitly output (display) referred with an average gamma of 2.2.) [6]

The Rec. 709 transfer function from the linear signal (luminance) to the nonlinear (voltage) is, similar to sRGB's transfer function, linear in the bottom part and then transfers to a power function for the rest of the $[0..1]$ range:[7]

$V=\begin{cases} 4.500L & L < 0.018\\ 1.099 L^{0.45} - 0.099 & L \ge 0.018 \end{cases}$

The conversion to linear is as follows.

$L=\begin{cases} \dfrac{V}{4.5} & V < 0.081\\ \left ( \dfrac{ V+0.099 }{ 1.099} \right ) ^{\frac{1}{0.45} } & V > 0.081 \end{cases}$