Working in BT.601, given the following 8bit values for Y, Cr and Cb, what RGB values should I expect when converted from Y Cr Cb to RGB?
Y = 168
Cb = 44
Cr = 136
For convenience, here are the BT.601 coefficients:
#Kr = 0.299: #Kg = 0.587: #Kb = 0.114
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Last edited by chris319; 24th Feb 2022 at 02:02.

Approx 75% Yellow (R=521.69mV, G=547.45mV, B=23.5mV  my assumption is YCbCr is limited quantization range and RGB full quantization range i.e. black = 0V and 100% is 700mV).
However seem you are confusing few things, YPbPr is video signal and as such it should be expressed as voltage (level) not number. YCbCr is expressed as number. Secondly if your goal was to get level in full or limited quantization range  you didn't provided this information so i've made some assumption. 
R=521.69 mV, G=547.45 mV, B=23.5 mV
521.69 / 700 = 0.74527
0.74527 * 256 = 190.7
The Pb and Pr numbers are 8bit values taken directly from Fig. 3.2, below:
http://car.france3.mars.free.fr/HD/INA%2026%20jan%2006/SMPTE%20normes%20et%20confs/rp...9%20mirehd.pdf
The numbers I am expecting to see are R ~ 180, G ~ 180, B ~ 16. Is there a way to calculate this to get numbers closer to those expected? I'm not sure if I'm dealing with full or limited range. Also, there is a remote possibility that those Y, Pr, Pb numbers are for BT.709.Last edited by chris319; 21st Feb 2022 at 18:47.

YUV "709":
YUV limited '709', rgb full out would be: 191,191,0
YUV full '709', rgb full out would be: 181,180,12
YUV limited '709', rgb limited out would be: 180,180,16
YUV full '709', rgb limited out would be: 171,171,26
YUV "601":
YUV limited '601', rgb full out would be: 190,203,8
YUV full '601', rgb full out would be: 179,191,19
YUV limited '601', rgb limited out would be: 179,191,22
YUV full '601', rgb limited out would be: 170,180,32
values are rounded +1 or so
so your numbers would match limited "709" values YUV in and limited RGB out calculations 
YUV limited '709', rgb limited out would be: 180,180,16
The version of the RP 219 spec I have is from 2002 so it's possible those Y Pr Pb values were revised at some point to conform to BT.709, perhaps being for BT.601 in previous versions. 
I do not have equations, using vapoursynth resize filter, once I really calculate it manually to prove that vs does that the same as your provided equations would, but that time, it was limited YUV 709 to full RGB:
https://forum.videohelp.com/threads/39614010BitPixels/page2#post2575815
it would need to be changed to limited rgb 
Those values are for the 75% yellow limited range 709 bar. Upon conversion to full range RGB you should get about 191,191,0 (R,G,B). Converted to limited range RGB you should get about 180,180,12 (the blue channel should be 16 but rounding errors in the starting YCbCr cause it to drop). You already have the equations for this, we've covered it many times.

This code gets me close but is not very accurate:
Code:r = y + 2*(v128)*(1Kr) g = y  2*(u128)*(1Kb)*Kb/Kg  2*(v128)*(1Kr)*Kr/Kg b = y + 2*(u128)*(1Kb)
75% White
180
180
180
Yellow
181
180
12
Blue
15
16
184
Green
13
181
12
Magenta
183
15
184
Red
183
15
16
Cyan
13
181
180
The YUV values are canonical per SMPTE RP 219 spec. 
Thank you, Sharc. This seems to get the values closer:
Code:r = 1.164 * (y16) + 0 * (u128) + 1.793 * (v127): r + 16: r = Int(r * 0.867) g = 1.17 * (y16) + 0.213 * (u128) + 0.533 * (v128): g + 16: g = Int(g * 0.867) b = 1.164 * (y16) + 2.1 * (u128): b + 16: b = Int(b * 0.867)
R 236
G 236
B 234
Yellow
R 181
G 179
B 14
Blue
R 15
G 14
B 178
Green
R 15
G 179
B13
Magenta
R 181
G 14
B 179
Red
R 181
G 14
B 14
Cyan
R 15
G 180
B 178 
"Studio RGB" aka "Limited Range RGB"
709
R = Y + 1.54(Cr128)
G = Y  0.459(Cr128)  0.183(Cb128)
B = Y + 1.816(Cb128)
601
R = Y + 1.371(Cr128)
G = Y  0.698(Cr128)  0.336(Cb128)
B = Y + 1.732(Cb128) 
From ITUR BT.7096 and BT6017 I concluded once almost identical:
709
R = Y + 1.5396(Cr128)
G = Y  0.4577(Cr128)  0.1831(Cb128)
B = Y + 1.8142(Cb128)
601
R = Y + 1.3707(Cr128)
G = Y  0.6982(Cr128)  0.3365(Cb128)
B = Y + 1.7324(Cb128)
(But I thought the OP asked for RGB<>YPbPr conversion, rather than RGB<>YCbCr) 
Those values are ok  obviously math is without saturation (not clamped between 16..235 and 16..240)  if you do proper clamping then everything will be fine.
This is my point  OP ask for YPbPr but provide numbers for YCbCr and there is no information about quantization range.
In YPbPr, Y should be within 0..700mV, Pb and Pr shall be within 350..+350mV range (and analog signals are always in same "full quantization range").
As such this is important to understand OP question and provide valid answer. 
I already explained this to you several posts ago, Pandy:
The Pb and Pr numbers are 8bit values taken directly from Fig. 3.2, below:
http://car.france3.mars.free.fr/HD/INA%2026%20jan%2006/SMPTE%20normes%20et%20confs/rp...9%20mirehd.pdf 
This code works even better. +/ 1. I must have missed it in BT.709.6
From ITUR BT.7096 and BT6017 I concluded once almost identical:
709
R = Y + 1.5396(Cr128)
G = Y  0.4577(Cr128)  0.1831(Cb128)
B = Y + 1.8142(Cb128)Code:100% White 235 235 235 Yellow 180 180 16 Blue 16 16 180 Green 16 180 15 Magenta 180 16 181 Red 180 16 17 Cyan 16 180 179
Last edited by chris319; 22nd Feb 2022 at 15:20.

Issue is naming convention  YPbPr shall be reported in voltages (corresponding YCbCr values can be presented in parallel)  YPbPr is real analog signal where YCbCr is digital domain (samples)  this is why it is confusing.
You can check ITUR BT.1361 and ITUR BT.801 + RREPBT.2380  not sure what naming convention is in US but in Europe this is quite strict. 
Issue is naming convention  YPbPr shall be reported in voltages (corresponding YCbCr values can be presented in parallel)  YPbPr is real analog signal where YCbCr is digital domain (samples)  this is why it is confusing.

So you're saying...be strict about the numbers but not about the terms they refer to?
It seems inconsistent.
Scott 





I hate it when people give only the final matrix equations for complex conversions. They're are nice for coding but do not elucidate where all the coefficients come from.
The Kr, Kg, Kb coefficients are for rec.601 but your "YPbPr" values are for limited range rec.709 YCbCr. And they are rounded to the nearest integer. If you use the reciprocal equation and floating point for all the calculations you'll see that the actual limited range values for R=191, G=191, B=0 are Y=168.192, U=44.110, V=135.692. The quoted conversion equation is for converting full range YUV to full range RGB.
The correct coefficients and equations for converting full range RGB to limited range YUV (YCbCr), and full range RGB to full range YUV are given at the aviSynth.nl:
http://avisynth.nl/index.php/Color_conversions
The correct way convert studio (limited range) RGB to limited range YUV is to first convert the studio RGB to full range RGB then convert to limited range YUV using those equations. To reverse the operation convert the YUV to full range RGB then convert the full range RGB back to limited range RGB.
Code:sRGB = each studio RGB component fRGB = each full range RGB component sRGB = fRGB * 219 / 255 + 16 fRGB = (sRGB16) * 255 / 219
Given those sRGB to fRGB equations and full range RGB to limited range YUV equations from from the AviSynth docs:
Code:Kr = 0.2126 Kg = 0.7152 Kb = 0.0722 y  16 = (Kr*219/255)*r + (Kg*219/255)*g + (Kb*219/255)*b v  128 = 112/255*r  Kg*112/255*g/(1Kr)  Kb*112/255*b/(1Kr) u  128 =  Kr*112/255*r/(1Kb)  Kg*112/255*g/(1Kb) + 112/255*b r = (255/219)*y + (255/112)*v*(1Kr)  (255*16/219 + 255*128/112*(1Kr)) g = (255/219)*y  (255/112)*u*(1Kb)*Kb/Kg  (255/112)*v*(1Kr)*Kr/Kg  (255*16/219  255/112*128*(1Kb)*Kb/Kg  255/112*128*(1Kr)*Kr/Kg) b = (255/219)*y + (255/112)*u*(1Kb)  (255*16/219 + 255*128/112*(1Kb))
First convert the sRGB to fRGB:
Code:R = (18016) * 255 / 235 ~= 191 G = (18016) * 255 / 235 ~= 191 B = (1616) * 255 / 235 = 0

The Kr, Kg, Kb coefficients are for rec.601 but your "YPbPr" values are for limited range rec.709 YCbCr.
The correct way convert studio (limited range) RGB to limited range YUV 
I suggest something other than "sRGB" to indicate "studio" or limited range RGB, maybe "lRGB" ? "sRGB" is already taken as standard RGB
One issue with that method (for converting limited yuv to limited rgb) is original Y values <16, >235 will be clipped at the first step. One of the touted "benefits" for using studio RGB (instead of sRGB) is preserving the foot/head room. If you do the conversion in zimg/vapoursynth, or Sony Vegas studio RGB, the original values that were Y <16, >235 are visible. I do not believe converting to full range RGB first is correct, or at least it's different than what the "studio RGB" is in Vegas
EDIT:
Looking at this more closely:
My bad; this works if you run it in float . I think internally what you describe is what is happening in vegas and zimg (avsresize in avs) . expr (reverse polish notation) for the math in float, but using 8bit reference numbers, can be used with scale_inputs = "float"
In avs
#YV24 source (to eliminate subsampling differences)
ConvertBits(32)
ConvertToPlanarRGB(chromaresample="point", matrix="rec709")
expr("x 219 * 255 / 16 +", "x 219 * 255 / 16 +", "x 219 * 255 / 16 +", scale_inputs = "float")
ConvertBits(8)
or
#YV24 source (to eliminate subsampling differences)
z_ConvertFormat(pixel_type="RGB24", resample_filter="point", colorspace_op="709:709:709:l=>rgb:709:709:l")
These give the same results, and no range clipping that you get in 8bit RGB for the 1st stepLast edited by poisondeathray; 23rd Feb 2022 at 22:14.


why does your topic title refer to analog values?
I have changed the OP to Y Cb Cr. Now will you STFU?
Don't be surprised if you hear from a moderator. I have reported your post.Last edited by chris319; 24th Feb 2022 at 02:07.

All right. That's how I did it:
I took the matrix coefficients for R'G'B' > Y'CbCr conversion from ITUR BT.7096, formula 3.5. For 8bit n=8.
[Attachment 63534  Click to enlarge]
Then I inverted the matrix to obtain Y'CbCr > R'B'G' which gave the coefficients of post #13 and #21
All in floating point, no integer rounding.
Added:
For what it's worth, here a calculator. It doesn't explain its maths under the hood though, but at a first glance it seems to return identical values as my matrix formula of post #13 or #21.
https://res18h39.netlify.app/colorLast edited by Sharc; 24th Feb 2022 at 04:12. Reason: Link added
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