# [FFmpeg-devel] [PATCH 2/3] lavd: add teletext quantizer

Michael Niedermayer michael at niedermayer.cc
Thu Jan 14 00:11:35 CET 2016

```On Thu, Jan 14, 2016 at 01:41:51AM +0300, Andrey Turkin wrote:
> 2016-01-13 22:32 GMT+03:00 Michael Niedermayer <michael at niedermayer.cc>:
>
> > to calculate the phase
> >
> > the area that has alternating 0/1 values can be correlated with a
> > sin() and a cos(), if you consider the 2 resulting values as x and y
> > coordinates the angle they form from the origin is the phase.
> > (this can be worded simpler using complex numbers)
> >
> > when above is done its essential that a whole multiple of cycles is
> > used the important part is that the used sin(x) and cos(x) vectors are
> > orthogonal, that is sum sin(x) * cos(x) over the x values considered is
> > 0 cutting them off randomls would break that
> > (its also possible to use windowing instead of a exact multiple of cycles)
> >
> > consider that the phase is 0 so our signal input is exactly
> > cos(x) (if we define that as 0°), the dot product of that with cos(x)
> > is "1" and sin(x) is 0
> > now if our input is shifted by 90deg that is it matches sin(x)
> > then the dot product with a cos(x) vector is 0 and sin(x) is 1
> > ...
> > (also i for simpliity normalized the values, sum of cos(x)*cos(x) for
> > x from 0 to n would of course be larger than 1 for a larger n)
> >
>
> That should work; I wonder about runtime cost though. sin/cos for a given
> frequency can be precomputated; atan2 can be turned to table or something.
> Still there'd be about 32 multiplications to get a phase (over 4 periods).
> That's more than 25000 multiplications per second per teletext standard.

25000 operations per second is not much, copying the images takes
orders of magnitude more

[...]
--

The bravest are surely those who have the clearest vision
of what is before them, glory and danger alike, and yet
notwithstanding go out to meet it. -- Thucydides
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