[FFmpeg-user] Glossary: Nyquist

[Anatoly]

On Wed, 30 Sep 2020 19:21:59 -0400
"Mark Filipak (ffmpeg)" <markfilipak at bog.us> wrote:

> Nyquist [adjective]: 1, Reference to the Nyquist-Shannon sampling
>    theorem. 2, The principle [1] that, to most faithfully reproduce an
>    image at a given digital display's resolution, the samples must be
>    made at or above twice the display's resolution, both horizontally
> & vertically [2].
Sorry, but this is wrong.
from
https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
"If a function x(t) contains no frequencies higher than B hertz, it is
completely determined by giving its ordinates at a series of points
spaced 1/(2B) seconds apart.
A sufficient sample-rate is therefore anything larger 2B samples per
second."
Let's say we have 640 horisontal dots (pixels) per line in NTSC system.
So imagine NTSC analogue (CRT) camera that shots image of thin
alternating black and white vertical stripes. Let say there is 320
white and 320 black stripes, 640 stripes total. This picture produces
maximum possible frequency in analogue video signal.
One TV line is 64uS. Blanking interval is 12uS. Visible line is
64-12=52uS. This interval in our case is filled with square (ideally)
wave. So what is period of this wave? It is of two of those vertical
stripes. Onle line is black (negative half-wave) and one white (positive
half-wave). So what is frequency of that signal?
1/(52*10^-6)*640/2=6153846Hz or 6.15Mhz and this is our B
(Real analogue B/G TV system has slightly lower bandwidth)
According to Nyquist-Shannon we must sample at 2B or 12.3Mhz.
But what is 2B? It is one sample per one vertical stripe (black or
white), or one image dot (pixel).
640 dots per line we want to reproduce = 640 samples per line we must
take
So it is one sample per pixel.