[FFmpeg-user] Glossary: Nyquist

[Mark Filipak (ffmpeg)]

Correction:
"if your sampling frequency exceeds Nyquist" was "if your sampling frequency exceeds Nyquist/2" 
(which was an inadvertent mistake). Sorry.


On 10/04/2020 09:44 PM, Anatoly wrote:
> On Sun, 4 Oct 2020 10:37:41 -0400
-snip-
> Are you watched "Part 2" ?
> https://www.youtube.com/watch?v=ht4Mv2wIRyQ
> 
>> I don't think spacial image resolution is
>> related to frequency at all.
> Then watch mentioned above video at 8:07
> He didnt explain this, but those plots actually is so called frequency
> responces (attenuation vs frequency).
> What do you see on upper plot there?

What the upper graph shows is the frequency response of the serial bitstream from the photosite 
array through the analog-to-digital converter. Nyquist does indeed apply to that, but only because 
the camera forms the samples in a limited amount of time and the analog-to-digital converter is 
multiplexed (shared) by the photosites -- Fo is the sampling frequency, so the resolution of the 
analog-to-digital converter is artificially limited (filtered) to Fo/2. But that is not directly a 
property of the picture's resolution. It's a property of the camera design that limits the camera's 
resolution. Pictures are not made of sine waves. Coded pictures are DCT encoded but Nyquist has 
nothing to do with that part because DCT is done entirely in the digital domain, after sampling, and 
time is not a factor in the digital domain.

The sampling system limits resolution, yes. And that limit is Fo/2, yes. But pictures don't have a 
Nyquist frequency, no matter what number of samples/line or lines/frame. And pictures are not made 
of sine waves. You are getting lost in the camera design.

> X axis is "spatial frequency / line pairs" as distance between two pairs
> of lines of picture of alternating black and white lines.

(line pairs)/(picture height) -- I assume "line pairs" means the horizontal distance between 
vertical lines -- is a pretty odd frequency scale, and calling that a spacial frequency is pretty 
bogus. The bottom line is this: Nyquist applies to serial analog-to-digital conversion frequency, 
not to the ultimate resolution. It says that if your sampling frequency exceeds Nyquist, you're 
going to get aliasing. That's the kernel of the presentation and you are misinterpreting what is 
being presented.

In other words, the Nyquist frequency is a function of each particular camera and the frequency at 
which that camera does analog-to-digital conversion.

The premise that to get 720x480, frames should be sampled at 1440x960 is bogus. I've read that so 
many times that I put it into the glossary without really thinking about it. But it's wrong.

Oh, and did I say that pictures are not made of sine waves?

-- 
What if you woke up and found yourself in a police state?
African-Americans wake up in a police state every day.
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