[FFmpeg-user] Glossary: Nyquist

Mark Filipak (ffmpeg) markfilipak at bog.us
Fri Oct 2 03:25:30 EEST 2020

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.
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.

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.

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