PAL (Phase Alternation by Line) was developed to fix NTSC (National Television System Committee) problems with color. Each PAL frame consist of 625 lines, 25 frames per second. All image data is in scan-lines.

Pic 1. Normal scanline.

Pic 2. Vertical retraces.

Color in PAL is coded using YUV colorspace model, where Y stands for luminance (brightness), and U V stands for chrominance. This is not the usual way that we used to represent color information (like RGB or CMYK models). The fact that we are using this method is mainly because the inventors of PAL had to made it compatible with older black&white television systems.

Pic 3. YUV colorspace.

[ Y ]   [ 0.299  0.587  0.114 ] [ R ] [ U ] = [-0.147 -0.289  0.436 ]*[ G ] [ V ]   [ 0.615 -0.515 -0.100 ] [ B ] [ R ]   [ 1  0      1.14  ] [ Y ] [ G ] = [ 1 -0.394 -0.581 ]*[ U ] [ B ]   [ 1  2.028  0     ] [ V ] Pic 4. RGB to YUV conversions.

In fact, there is no possibility for video-decoder to discover the phase of signal. This information is sent every line during color-burst phase, when transmitter sends the sinus signal with correct phase. That allows receiver to synchronise phase every line.

Most projects with microcontroler PAL generation are based on equation:

  a sin(x) + b cos(x) = A sin (x + B),
  A= sqrt( a^2 + b^2 ), tg(B) = a/b

Simply:

why we have to calculate sinus and cosinus functions for each sample when we can only calculate one sinus with phase shift?

I decided to go some other way. Since my microcontroler is running four times as fast as the color signal, I simply write four equations for each sample of signal:

  S0 = Y + U cos(2pi*0/4) +/- V sin (2pi*0/4)
  S1 = Y + U cos(2pi*1/4) +/- V sin (2pi*1/4)
  S2 = Y + U cos(2pi*2/4) +/- V sin (2pi*2/4)
  S3 = Y + U cos(2pi*3/4) +/- V sin (2pi*3/4)

In fact, the values of cos and sin are well known for this angles so we get...

  S0 = Y + U
  S1 = Y +/- V
  S2 = Y - U
  S3 = Y -/+ V

...what is very easy to calculate, even real-time.

Simply:

why we have to calculate sinus function for each sample when we can only add or subtract values?

But there is still one problem with this solution - when I generating color signal I don't have time to do anything else. That's bad. We cannot make loops and other things. So I tried to make color with 2 samples only, but without changing color-burst. First I tested it in device and it works, so I went back to paper to find out what am I really doing ... ;) To solve this problem we have to know that PAL color signal is same for two horizontal lines - odd and even pair. The decoder is applying addition operation to them to get the U, and substraction to get the V. So in fact we at start got 4 samples:

(S00, S01) at first line
(S10, S11) at second line

when we add and subtract them we got pairs:

U: (S00+S10, S01+S11)
V: (S00-S10, S01-S11)

So, basically we are modulating U and V by using 2 samples for each. In fact, the thing that is important is fact that we can control the amplitude of them, which is:

U = S01+S11 - (S00+S11)
V = S01-S11 - (S00-S10) = S01+S10 - (S00+S11)

Simply:

why we have to modulate 8 samples to get the color for two pixels when we can only use 4 samples and have free time then?

Equations are simplified to illustrate the idea.