[FFmpeg-user] Glossary: Nyquist

Eduardo Alarc├│n ealarcong at gmail.com
Fri Oct 2 21:15:30 EEST 2020

El vie., 2 oct. 2020 a las 7:34, Anatoly (<anatoly at kazanfieldhockey.ru>)

> On Thu, 1 Oct 2020 20:25:30 -0400
> "Mark Filipak (ffmpeg)" <markfilipak at bog.us> wrote:
> > On 10/01/2020 07:43 PM, Anatoly wrote:
> > > 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.
> > -snip-
> > Yes, yes, of course. You are correct, but this is different.
> >
> > The source is not an NTSC analog signal. The source is analog streams
> > of photons striking a CCD imager array, frame by frame, and applies
> > to the image regardless whether the image is moving or stationary,
> > and regardless of exposure time (which affects brightness, not
> > resolution). The source is a 2-dimensional, lighted field of view in
> > a camera or film scanner transferring light energy to produce charge
> > in photo transistors over a spacial area. It's not temporal as is the
> > case when sampling a changing analog voltage.
> Yet I think replacing Voltage with Light Intencity and Time with X
> coordinate on analoguie video signal graph changes nothing, if you are
> about moving to spatial domain.
> >
> > When sampling an analog voltage, resolution is the ability to resolve
> > voltage value within a certain period of time (i.e. within a given
> > channel bandwidth). When sampling a visual field of view however,
> > resolution is the ability to resolve stationary edges that vary
> > spacially, going from light to dark or dark to light. It's the same
> > gaussian energy transfer issue (i.e. that transferring energy
> > requires time) with the same signal-to-noise issues and the same
> > handy half-power shorthand, but it applies to ... wait for it ...
> > human eyes! Human eyes resolve edges only so good, even totally black
> > abutting totally white. There is nothing you can do about that, and
> > staring at the edge doesn't bring it into higher resolution. However,
> > if the image source itself has fuzzy edges because it was sampled at
> > lower than Nyquist, then the result in our brains is a double
> > gaussian, the first from the CCD and the second from our eyes. It's
> > that double gaussian that is avoided by spacially sampling at higher
> > than 2x the display resolution.
> >
I think this is wrong, Nyquist theorem or principles apply to sampling of a
signal, nothing to do with eyes or brain, it describes the minimum sampling
rate that permits the conversion of an analog signal to a digital one that
can be reconstructed unequivocally with said sampling data.
In audio, if you have a 10 khz signal you need to sample it at 20khz to be
able to reconstruct it later. Any signal of higher frequency will not be
correctly reconstructed, that's one of the reasons cd audio is sampled at
44.1 khz
In images the need to sample at a higher resolution (double the resolution)
makes sense, but I don't know if this is how the CCDs really work.
Human perception, brain interpretation, human psychology have nothing to do
with Nyquist.

> So you want to say that if I watching picture on 640x480 dots
> display, my brain "effectively" can percept only 320x240 dots. And for
> my brain to percept "effectively" 640x480, I need 1280x960 from CCD to
> LCD?
> Then I may say that at image processing domain such a terms as "640x480"
> or "4K" is all about real count of pixels (spatial samples), not about
> how human brain will percept them. So if you're writing about human
> perception, you probably must state it explicitly. I can't duscuss about
> human perception because I know little here.

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