Editing Y′UV (section)

=== SDTV with BT.470 ===
Y′UV signals are typically created from [[RGB color model|RGB]] ([[red]], [[green]] and [[blue]]) source. Weighted values of R, G, and B are summed to produce Y′, a measure of overall brightness or luminance. U and V are computed as scaled differences between Y′ and the B and R values.

PAL (NTSC used [[YIQ]], which is further rotated) standard defines the following constants,<ref>{{cite web |title=BT.470: Conventional television systems |url=https://www.itu.int/rec/R-REC-BT.470-6-199811-S/en |access-date=2021-04-16 |website=www.itu.int |page=9}}</ref> derived from BT.470 System M primaries and white point using SMPTE RP 177 (same constants called matrix coefficients were used later in [[YCbCr#ITU-R BT.601 conversion|BT.601]], although it uses 1/2 instead of 0.436 and 0.615):

:<math>\begin{align}
           W_R &= 0.299, \\
           W_G &= 1 - W_R - W_B = 0.587, \\
           W_B &= 0.114, \\
  U_\text{max} &= 0.436, \\
  V_\text{max} &= 0.615.
\end{align}</math>

PAL signals in Y′UV are computed from R'G'B' (only SECAM IV used linear RGB<ref name=SECAM4>{{cite web |date=2019-02-27 |title=World Analogue Television Standards and Waveforms |url=http://www.radios-tv.co.uk/Pembers/World-TV-Standards/Colour-Standards.html#SECAM |url-status=live |access-date=2021-04-16 |archive-url=https://web.archive.org/web/20190227232952/http://www.radios-tv.co.uk/Pembers/World-TV-Standards/Colour-Standards.html#SECAM |archive-date=27 February 2019}}</ref>) as follows:

:<math>\begin{align}
  Y' &= W_R R' + W_G G' + W_B B' = 0.299 R' + 0.587 G' + 0.114 B', \\
   U &= U_\text{max} \frac{B' - Y'}{1 - W_B} \approx 0.492(B' - Y'), \\
   V &= V_\text{max} \frac{R' - Y'}{1 - W_R} \approx 0.877(R' - Y').
\end{align}</math>

The resulting ranges of Y′, U, and V respectively are [0, 1], [−''U''<sub>max</sub>, ''U''<sub>max</sub>], and [−''V''<sub>max</sub>, ''V''<sub>max</sub>].

Inverting the above transformation converts Y′UV to RGB:

:<math>\begin{align}
  R' &= Y' + V \frac{1 - W_R}{V_\text{max}} = Y' +  \frac{V}{0.877} = Y' +  1.14 V,\\
  G' &= Y' - U \frac{W_B (1 - W_B)}{U_\text{max} W_G} - V \frac{W_R (1 - W_R)}{V_\text{max} W_G} \\
    &= Y' - \frac{0.232 U}{0.587} -  \frac{0.341 V}{0.587} = Y' - 0.395 U - 0.581 V, \\
  B' &= Y' + U \frac{1 - W_B}{U_\text{max}} = Y' +  \frac{U}{0.492} = Y' +  2.033 U.
\end{align}</math>

Equivalently, substituting values for the constants and expressing them as [[Matrix (mathematics)|matrices]] gives these formulas for BT.470 System M (PAL):

:<math>\begin{align}
  \begin{bmatrix} Y' \\ U \\ V \end{bmatrix}
  &=
  \begin{bmatrix}
    0.299   &  0.587   &  0.114 \\
   -0.14713 & -0.28886 &  0.436 \\
    0.615   & -0.51499 & -0.10001
  \end{bmatrix}
  \begin{bmatrix} R' \\ G' \\ B' \end{bmatrix}, \\

  \begin{bmatrix} R' \\ G' \\ B' \end{bmatrix}
  &=
  \begin{bmatrix}
  1 &  0       &  1.13983 \\
  1 & -0.39465 & -0.58060 \\
  1 &  2.03211 &  0
  \end{bmatrix}
  \begin{bmatrix} Y' \\ U \\ V \end{bmatrix}.
\end{align}</math>

For small values of Y' it is possible to get R, G, or B values that are negative so in practice we clamp the RGB results to the interval [0,1] or more correctly clamp inside the Y'CbCr.

In BT.470 a mistake was made because 0.115 was used instead of 0.114 for blue and 0.493 was the result instead of 0.492. In practice that did not affect the decoders because the approximation 1/2.03 was used.<ref>{{cite journal |title=ST 170:2004 - SMPTE Standard - For Television — Composite Analog Video Signal — NTSC for Studio Applications |url=https://ieeexplore.ieee.org/document/7291416 |archive-url=https://web.archive.org/web/20180608112731/https://ieeexplore.ieee.org/document/7291416/ |url-status=dead |archive-date=8 June 2018 |journal=St 170:2004 |date=November 2004 |pages=1–21 |doi=10.5594/SMPTE.ST170.2004|isbn=978-1-61482-335-3}}</ref>