[FFmpeg-user] Glossary: Nyquist

[Mark Filipak (ffmpeg)]

On 10/03/2020 05:12 PM, Michael Koch wrote:
> Am 03.10.2020 um 22:43 schrieb Mark Filipak (ffmpeg):
>> On 10/03/2020 02:05 PM, Anatoly wrote:
>>> On Sat, 3 Oct 2020 11:05:03 -0400
>> -snip-
>>> You should learn than what spectrum is.
>>
>> Oh, please. Be easy with me. I'm just a simple electrical engineer.
>>
>>> And how any complex waveform
>>> (with it's "information density") may be represented as a sum of many
>>> simple sinewaves.
>>
>> Ah, now that would be a Taylor series, no?
> 
> Joseph Fourier just turned around in his grave...
> 
> Michael

Well, I've done some reading and it appears I need to tuck my tail between my legs and slink away. 
 From what I've read, Nyquist sampling is in the frequency domain, but I honestly don't see how 
Fourier applies to spacial resolution, even given that MTF is used to characterize CCD and CMOS 
response. Bear with me now...

Here's what I visualize:
Imagine a heat map -- one of those colorful images ...reds and yellows and greens and blues. Then, 
imagine a screen in front of it, between you and the heat map. The screen is the final samples (ex: 
720x480). The underlying heat map could also be 720x480, but if it is of higher resolution (ex: 
1440x960), then the slope of color changes in the heat map are more precise and the positions of the 
true colors that show through the screen (manifested as more accurate values) are slightly more 
accurate. It's equivalent to rescreening a screened print image (ex: 200 dpi rescreened to 100 dpi).

I think you'll agree that neither the screen nor the underlying heat map are serial in nature. Oh, 
they're transported as a sort-of raster -- that's for sure -- but that's not how they're made and I 
don't think that Fourier applies.

The reason I cite a heat map rather than an ordinary image is that it makes it easier to visualize 
the image formed as an energy distribution; an energy map if you will -- heat is energy.

The physical response to energy is not instantaneous. Responding to energy change requires time, and 
looking up & down or left & right, for example, exposes your eyes to changing energy. So it's a 
2-step process: 1, the response of the sampling process to the underlying heat map, and 2, the 
response of your eyes to the content of the samples (i.e. the screen). That's what I meant by double 
gaussian.

Why gaussian? Every real case of energy transfer that I've seen (outside of quantum mechanics) is 
ruled and regulated by gaussian factors, from fluid flow to capacitor charge. Is the exponential 
function gaussian. Gosh, I think so, but I can't find any justification right now.

I've consulted my copy of Feynman but he didn't have anything to say about Nyquist.

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