## Introduction

BT.709 is also known by the abbreviations Rec. 709. It standardizes the format of high-definition television, having 16:9 (widescreen) aspect ratio. YPbPr color model used in analog component video and its digital version YCbCr used in digital video.Y′ stands for the luma component (the brightness) and U and V are the chrominance (color) components. Luminance is denoted by Y and luma by Y′. Prime symbols (‘) denote gamma compression, with Luminance meaning physical linear-space brightness, while Luma is (nonlinear) perceptual brightness.

## Conversion Coefficients

Luminance is defined as a weighted sum of the color components. Weighted values of R, G, and B are summed to produce Y′. U and V are computed as scaled differences between Y′ and the B and R values.

Kg = 1- Kr - Kb

Y = Kr*R + Kg*G + Kb*B
V = (R-Y)/(1-Kr) = R - G * Kg/(1-Kr) - B * Kb/(1-Kr)
U = (B-Y)/(1-Kb) = - R * Kr/(1-Kb) - G * Kg/(1-Kb) + B

R = Y + V*(1-Kr)
G = Y - U*(1-Kb)*Kb/Kg - V*(1-Kr)*Kr/Kg
B = Y + U*(1-Kb)

Values of Kr, Kb and Kg are

Y′= 0.2126 R' + 0.7152G' + 0.0722B'

## BT.709 Conversion Matrix

R’G’B’ and Y’PbPr is ranging from 0 to 1. R’G’B’ reference black is zero and reference white is unity. Conversion matrix are

First row of top equation (R’G’B’ to Y’PbPr conversion matrix) comprises the luma coefficients; these sum to unity. The second and third rows each sum to zero, a necessity for color difference components.

## RGB To YCbCr Conversion

In 8-bit systems, a luma offset of +16 is added at the interface, placing black at code 16 and white at code 235. An offset of +128 is added to Cb and Cr, yielding a range of 16 through 240 inclusive. In a 10-bit interface, the 8-bit interface levels and prohibited codes are maintained; the extra two bits are appended as least-significant bits to provide increased precision. To obtain Y’CbCr from R’G’B’ ranging 0 to 1, scale the rows of the matrix in Equation 0 by the factors [219, 224, 224], corresponding to the excursions of each of the components.

In the 8-bit encoding, R’, B’, G’, and Y’ channels have a range of [16..235], and the Cb and Cr channels have a range of [16..240]. So in R’G’B’, reference black is [16, 16, 16] and reference white is [235, 235, 235]. In Y’CbCr, reference black is [16, 128, 128], and reference white is [235, 128, 128]. Values 0 and 255 are reserved as timing references, and may not contain color data. BT.709 nominal ranges are the same as those defined in BT.601.

## Studio RGB To YCbCr

In studio equipment, 8-bit R’G’B’ components have the same 219 excursion as the luma component of Y’CbCr. To encode 8-bit Y’CbCr from R’G’B’ in the range [0…219], scale the above matrix by (256/219).

## Computer RGB To YCbCr

Black is at code 0 and white is at 255 if 8-bit R’G’B’ components has no headroom and no footroom. To encode 8-bit Y’CbCr from R’G’B’ in this range [0….255], scale the matrix of Equation1 by (256/255) i.e.