Glossary: Nyquist

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Glossary: Nyquist

Mark Filipak (ffmpeg)
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].
   [1] The Nyquist principle applies to film sampling and to digital
       cameras, but, provided that resolution is unchanged, not to
       transcoding (because the transcoder inputs are already digital).
       As proved by the improved appearance of SD media made from 2K
       samples, SD mastering prior to the advent of 2K sampling (e.g.
       DVDs mastered before the advent of HD) generally ignored the
       Nyquist principle and were undersampled. HDs sampled at 2K and
       UHDs sampled at 4K are likewise undersampled.
   [2] As a convenience, the Nyquist threshold is currently (in 2020)
       specified solely by horizontal sample count rounded up to whole
       kilo-samples (2K, 4K, 8K).
                         display    Nyquist threshold
       UHD 16:9-2160:  3840 x 2160         8K
            4:3-2160:  2880 x 2160         8K
        HD 16:9-1080:  1920 x 1080         4K
            4:3-1080:  1440 x 1080         4K
        SD  16:9-576:  1024 x 576          4K
             4:3-576:   768 x 576          2K
            16:9-480:   853 x 480          2K
             4:3-480:   640 x 480          2K

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Re: Glossary: Nyquist

Eduardo Alarcón
Nyquist is a noun, not an adjective, for Harry Nyquist. The Nyquist–Shannon
sampling theorem is applicable to analog to digital conversion of signals
(continuous to discrete), images are a type of signal.

El mié., 30 sept. 2020 a las 20:25, Mark Filipak (ffmpeg) (<
[hidden email]>) escribió:

> 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].
>    [1] The Nyquist principle applies to film sampling and to digital
>        cameras, but, provided that resolution is unchanged, not to
>        transcoding (because the transcoder inputs are already digital).
>        As proved by the improved appearance of SD media made from 2K
>        samples, SD mastering prior to the advent of 2K sampling (e.g.
>        DVDs mastered before the advent of HD) generally ignored the
>        Nyquist principle and were undersampled. HDs sampled at 2K and
>        UHDs sampled at 4K are likewise undersampled.
>    [2] As a convenience, the Nyquist threshold is currently (in 2020)
>        specified solely by horizontal sample count rounded up to whole
>        kilo-samples (2K, 4K, 8K).
>                          display    Nyquist threshold
>        UHD 16:9-2160:  3840 x 2160         8K
>             4:3-2160:  2880 x 2160         8K
>         HD 16:9-1080:  1920 x 1080         4K
>             4:3-1080:  1440 x 1080         4K
>         SD  16:9-576:  1024 x 576          4K
>              4:3-576:   768 x 576          2K
>             16:9-480:   853 x 480          2K
>              4:3-480:   640 x 480          2K
>
> --
> What if you woke up and found yourself in a police state?
> African-Americans wake up in a police state every day.
> _______________________________________________
> ffmpeg-user mailing list
> [hidden email]
> https://ffmpeg.org/mailman/listinfo/ffmpeg-user
>
> To unsubscribe, visit link above, or email
> [hidden email] with subject "unsubscribe".
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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
On 10/01/2020 01:20 AM, Eduardo Alarcón wrote:
> Nyquist is a noun, not an adjective, for Harry Nyquist. ...

Hi Eduardo, Thanks.

Well, technically, a noun used as an adjective: "Nyquist sampling", makes it an adjective, but no
matter.

What if I narrow the scope to solely the sampling theory? thusly:

Nyquist sampling: The principle [1] that, to most faithfully reproduce
   an image at a given digital display's resolution, samples must be
   made at or above twice the display's resolution, both horizontally &
   vertically [2].
   [1] The Nyquist principle applies to film sampling and to digital
       cameras, but, provided that resolution is unchanged, not to
       transcoding (because the transcoder inputs are already digital).
       As proved by the improved appearance of SD media made from 2K
       samples, SD mastering prior to the advent of 2K sampling (e.g.
       DVDs mastered before the advent of HD) generally ignored the
       Nyquist principle and were undersampled. HDs sampled at 2K and
       UHDs sampled at 4K are likewise undersampled.
   [2] As a convenience, the Nyquist threshold is currently (in 2020)
       specified solely by horizontal sample count rounded up to whole
       kilo-samples (2K, 4K, 8K).
                         display    Nyquist threshold
       UHD 16:9-2160:  3840 x 2160         8K
            4:3-2160:  2880 x 2160         8K
        HD 16:9-1080:  1920 x 1080         4K
            4:3-1080:  1440 x 1080         4K
        SD  16:9-576:  1024 x 576          4K
             4:3-576:   768 x 576          2K
            16:9-480:   853 x 480          2K
             4:3-480:   640 x 480          2K

>... The Nyquist–Shannon
> sampling theorem is applicable to analog to digital conversion of signals
> (continuous to discrete), images are a type of signal.

Well, I thought that was what I wrote. What doesn't work for you?

The reason I wrote "both horizontally & vertically" was to resolve that, unlike sampling a
1-dimensional (serial) signal, 2-dimensional sampling (e.g. from film) or within a camera, requires
the Nyquist principle be applied in both dimensions. But perhaps that's not what you find lacking.
Could you suggest different wording maybe?

--
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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Re: Glossary: Nyquist

Eduardo Alarcón
Mostly the noun/adjective part, the part [1] about SD media and mastering,
seems to be anecdotal information more than a definition of what is the
Nyquist principle, you say that the images are undersampled, but what does
it mean? what is the impact, the images look blurry?, may be you defined
"undersampling" in other part


El jue., 1 oct. 2020 a las 11:18, Mark Filipak (ffmpeg) (<[hidden email]>)
escribió:

> On 10/01/2020 01:20 AM, Eduardo Alarcón wrote:
> > Nyquist is a noun, not an adjective, for Harry Nyquist. ...
>
> Hi Eduardo, Thanks.
>
> Well, technically, a noun used as an adjective: "Nyquist sampling", makes
> it an adjective, but no
> matter.
>
> What if I narrow the scope to solely the sampling theory? thusly:
>
> Nyquist sampling: The principle [1] that, to most faithfully reproduce
>    an image at a given digital display's resolution, samples must be
>    made at or above twice the display's resolution, both horizontally &
>    vertically [2].
>    [1] The Nyquist principle applies to film sampling and to digital
>        cameras, but, provided that resolution is unchanged, not to
>        transcoding (because the transcoder inputs are already digital).
>        As proved by the improved appearance of SD media made from 2K
>        samples, SD mastering prior to the advent of 2K sampling (e.g.
>        DVDs mastered before the advent of HD) generally ignored the
>        Nyquist principle and were undersampled. HDs sampled at 2K and
>        UHDs sampled at 4K are likewise undersampled.
>    [2] As a convenience, the Nyquist threshold is currently (in 2020)
>        specified solely by horizontal sample count rounded up to whole
>        kilo-samples (2K, 4K, 8K).
>                          display    Nyquist threshold
>        UHD 16:9-2160:  3840 x 2160         8K
>             4:3-2160:  2880 x 2160         8K
>         HD 16:9-1080:  1920 x 1080         4K
>             4:3-1080:  1440 x 1080         4K
>         SD  16:9-576:  1024 x 576          4K
>              4:3-576:   768 x 576          2K
>             16:9-480:   853 x 480          2K
>              4:3-480:   640 x 480          2K
>
> >... The Nyquist–Shannon
> > sampling theorem is applicable to analog to digital conversion of signals
> > (continuous to discrete), images are a type of signal.
>
> Well, I thought that was what I wrote. What doesn't work for you?
>
> The reason I wrote "both horizontally & vertically" was to resolve that,
> unlike sampling a
> 1-dimensional (serial) signal, 2-dimensional sampling (e.g. from film) or
> within a camera, requires
> the Nyquist principle be applied in both dimensions. But perhaps that's
> not what you find lacking.
> Could you suggest different wording maybe?
>
> --
> What if you woke up and found yourself in a police state?
> African-Americans wake up in a police state every day.
> _______________________________________________
> ffmpeg-user mailing list
> [hidden email]
> https://ffmpeg.org/mailman/listinfo/ffmpeg-user
>
> To unsubscribe, visit link above, or email
> [hidden email] with subject "unsubscribe".
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Re: Glossary: Nyquist

Mick Finn
In reply to this post by Mark Filipak (ffmpeg)
Most relevant to input sampling and not so relevant for displays unless higher spatial frequencies are actually present in data
Not to mention most cameras have optical low pass filters
In other words just beachside a 4k camera was used does not mean it can display alias free in 4k display
So please keep bad info off the list

Sent from my iPhone

> On Oct 1, 2020, at 9:18 PM, Mark Filipak (ffmpeg) <[hidden email]> wrote:
>
> On 10/01/2020 01:20 AM, Eduardo Alarcón wrote:
>> Nyquist is a noun, not an adjective, for Harry Nyquist. ...
>
> Hi Eduardo, Thanks.
>
> Well, technically, a noun used as an adjective: "Nyquist sampling", makes it an adjective, but no matter.
>
> What if I narrow the scope to solely the sampling theory? thusly:
>
> Nyquist sampling: The principle [1] that, to most faithfully reproduce
>  an image at a given digital display's resolution, samples must be
>  made at or above twice the display's resolution, both horizontally &
>  vertically [2].
>  [1] The Nyquist principle applies to film sampling and to digital
>      cameras, but, provided that resolution is unchanged, not to
>      transcoding (because the transcoder inputs are already digital).
>      As proved by the improved appearance of SD media made from 2K
>      samples, SD mastering prior to the advent of 2K sampling (e.g.
>      DVDs mastered before the advent of HD) generally ignored the
>      Nyquist principle and were undersampled. HDs sampled at 2K and
>      UHDs sampled at 4K are likewise undersampled.
>  [2] As a convenience, the Nyquist threshold is currently (in 2020)
>      specified solely by horizontal sample count rounded up to whole
>      kilo-samples (2K, 4K, 8K).
>                        display    Nyquist threshold
>      UHD 16:9-2160:  3840 x 2160         8K
>           4:3-2160:  2880 x 2160         8K
>       HD 16:9-1080:  1920 x 1080         4K
>           4:3-1080:  1440 x 1080         4K
>       SD  16:9-576:  1024 x 576          4K
>            4:3-576:   768 x 576          2K
>           16:9-480:   853 x 480          2K
>            4:3-480:   640 x 480          2K
>
>> ... The Nyquist–Shannon
>> sampling theorem is applicable to analog to digital conversion of signals
>> (continuous to discrete), images are a type of signal.
>
> Well, I thought that was what I wrote. What doesn't work for you?
>
> The reason I wrote "both horizontally & vertically" was to resolve that, unlike sampling a 1-dimensional (serial) signal, 2-dimensional sampling (e.g. from film) or within a camera, requires the Nyquist principle be applied in both dimensions. But perhaps that's not what you find lacking. Could you suggest different wording maybe?
>
> --
> What if you woke up and found yourself in a police state?
> African-Americans wake up in a police state every day.
> _______________________________________________
> ffmpeg-user mailing list
> [hidden email]
> https://ffmpeg.org/mailman/listinfo/ffmpeg-user
>
> To unsubscribe, visit link above, or email
> [hidden email] with subject "unsubscribe".
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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
In reply to this post by Eduardo Alarcón
On 10/01/2020 10:38 AM, Eduardo Alarcón wrote:
> Mostly the noun/adjective part, the part [1] about SD media and mastering,
> seems to be anecdotal information more than a definition of what is the
> Nyquist principle, you say that the images are undersampled, but what does
> it mean? what is the impact, the images look blurry?, may be you defined
> "undersampling" in other part

Thanks for your thoughts. They're important. Yes, I could write more. And, Yes, the note is
anecdotal. I felt that the note introduces the idea that something can be undersampled and with a
concrete example of something that is undersampled so that the concept becomes 'real'. Can you
suggest better wording? I'd like to see it.

Regarding what undersampling means, it's a common term that can be looked up in a general dictionary
rather than a dedicated glossary. That's just my opinion of course. Where do you think the line
should be drawn?

--
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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Re: Glossary: Nyquist

Eduardo Alarcón
El jue., 1 oct. 2020 a las 12:09, Mark Filipak (ffmpeg) (<[hidden email]>)
escribió:

> On 10/01/2020 10:38 AM, Eduardo Alarcón wrote:
> > Mostly the noun/adjective part, the part [1] about SD media and
> mastering,
> > seems to be anecdotal information more than a definition of what is the
> > Nyquist principle, you say that the images are undersampled, but what
> does
> > it mean? what is the impact, the images look blurry?, may be you defined
> > "undersampling" in other part
>
> Thanks for your thoughts. They're important. Yes, I could write more. And,
> Yes, the note is
> anecdotal. I felt that the note introduces the idea that something can be
> undersampled and with a
> concrete example of something that is undersampled so that the concept
> becomes 'real'. Can you
> suggest better wording? I'd like to see it.
>
> Me too, this is not my native language so i can not suggest a better
wording.


> Regarding what undersampling means, it's a common term that can be looked
> up in a general dictionary
> rather than a dedicated glossary. That's just my opinion of course. Where
> do you think the line
> should be drawn?
>
I think it should say that undersampling makes it look bad or blurry, so
that the concept is clear why it has to be that way.
Anyway it all depends on your target audience, if they have to know
concepts before or expect them to know nothing when reading your "manual".
That should define where the line is draw.

Off topic, i find your questions helpful or interesting at least on this
list, there are concepts i know and things i don't that i had to look up

> --
> What if you woke up and found yourself in a police state?
> African-Americans wake up in a police state every day.
> _______________________________________________
> ffmpeg-user mailing list
> [hidden email]
> https://ffmpeg.org/mailman/listinfo/ffmpeg-user
>
> To unsubscribe, visit link above, or email
> [hidden email] with subject "unsubscribe".
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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
On 10/01/2020 11:20 AM, Eduardo Alarcón wrote:
> El jue., 1 oct. 2020 a las 12:09, Mark Filipak (ffmpeg) (<[hidden email]>)
> escribió:
>
>> On 10/01/2020 10:38 AM, Eduardo Alarcón wrote:
-snip-
>> Can you suggest better wording? I'd like to see it.
>
> Me too, this is not my native language so i can not suggest a better wording.

Oh, you are doing fine. Trust me on this, being a native English speaker isn't all that it's cracked
up to be -- note the "cracked up" euphemism. :-)
I assume you're a native Spanish speaker. I think that Spanish is a very sensible and logical
language. English started out that way but got wrecked by the principle that anyone should be
allowed to do whatever they want.

-snip-
> I think it should say that undersampling makes it look bad or blurry, ...

Do you think the following -- changed "appearance" to "sharpness" & added "from film" in 2 places --
is improved and satisfies your desires?

[1] The Nyquist principle applies to film sampling and to digital cameras, but, provided that
     resolution is unchanged, not to transcoding (because the transcoder inputs are already
     digital). As proved by the improved sharpness of SD media made from 2K flim samples, SD
     mastering prior to the advent of 2K sampling (e.g. DVDs mastered from film before the advent
     of HD) generally ignored the Nyquist principle and were undersampled. HDs sampled from film
     at 2K and UHDs sampled from film at 4K are likewise undersampled.

> Off topic, i find your questions helpful or interesting at least on this
> list, there are concepts i know and things i don't that i had to look up

Is that "Off topic" in a user list dedicated to video processing? Really? Well, whatever the
opinion, I thank you for your kind words.

--
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African-Americans wake up in a police state every day.
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Re: Glossary: Nyquist

Eduardo Alarcón
El jue., 1 oct. 2020 a las 12:55, Mark Filipak (ffmpeg) (<[hidden email]>)
escribió:

> On 10/01/2020 11:20 AM, Eduardo Alarcón wrote:
> > El jue., 1 oct. 2020 a las 12:09, Mark Filipak (ffmpeg) (<
> [hidden email]>)
> > escribió:
> >
> >> On 10/01/2020 10:38 AM, Eduardo Alarcón wrote:
> -snip-
> >> Can you suggest better wording? I'd like to see it.
> >
> > Me too, this is not my native language so i can not suggest a better
> wording.
>
> Oh, you are doing fine. Trust me on this, being a native English speaker
> isn't all that it's cracked
> up to be -- note the "cracked up" euphemism. :-)
> I assume you're a native Spanish speaker. I think that Spanish is a very
> sensible and logical
> language. English started out that way but got wrecked by the principle
> that anyone should be
> allowed to do whatever they want.
>
> Yes, spanish speaker, well my name gives it away.

> -snip-
> > I think it should say that undersampling makes it look bad or blurry, ...
>
> Do you think the following -- changed "appearance" to "sharpness" & added
> "from film" in 2 places --
> is improved and satisfies your desires?
>
Yes, that makes more clear what is the importance of using it right.

>
> [1] The Nyquist principle applies to film sampling and to digital cameras,
> but, provided that
>      resolution is unchanged, not to transcoding (because the transcoder
> inputs are already
>      digital). As proved by the improved sharpness of SD media made from
> 2K flim samples, SD
>      mastering prior to the advent of 2K sampling (e.g. DVDs mastered from
> film before the advent
>      of HD) generally ignored the Nyquist principle and were undersampled.
> HDs sampled from film
>      at 2K and UHDs sampled from film at 4K are likewise undersampled.
>
> > Off topic, i find your questions helpful or interesting at least on this
> > list, there are concepts i know and things i don't that i had to look up
>
> Is that "Off topic" in a user list dedicated to video processing? Really?
> Well, whatever the
> opinion, I thank you for your kind words.
>

I meant off topic to this mail.

>
> --
> 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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> https://ffmpeg.org/mailman/listinfo/ffmpeg-user
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Re: Glossary: Nyquist

Greg Oliver
In reply to this post by Mark Filipak (ffmpeg)
On Wed, Sep 30, 2020 at 6:25 PM Mark Filipak (ffmpeg) <[hidden email]>
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].
>    [1] The Nyquist principle applies to film sampling and to digital
>        cameras, but, provided that resolution is unchanged, not to
>        transcoding (because the transcoder inputs are already digital).
>        As proved by the improved appearance of SD media made from 2K
>        samples, SD mastering prior to the advent of 2K sampling (e.g.
>        DVDs mastered before the advent of HD) generally ignored the
>        Nyquist principle and were undersampled. HDs sampled at 2K and
>        UHDs sampled at 4K are likewise undersampled.
>    [2] As a convenience, the Nyquist threshold is currently (in 2020)
>        specified solely by horizontal sample count rounded up to whole
>        kilo-samples (2K, 4K, 8K).
>                          display    Nyquist threshold
>        UHD 16:9-2160:  3840 x 2160         8K
>             4:3-2160:  2880 x 2160         8K
>         HD 16:9-1080:  1920 x 1080         4K
>             4:3-1080:  1440 x 1080         4K
>         SD  16:9-576:  1024 x 576          4K
>              4:3-576:   768 x 576          2K
>             16:9-480:   853 x 480          2K
>              4:3-480:   640 x 480          2K



Mark,

Normally I would absolutely defend your queries as they are technical and
lower level, but I would almost have to side with Bouke from post
(
bwdif filter question
)

You are trying to get free editing for your book now.  I do not agree with
that..  There are many good contributors and inquisitors (you included),
but (IMHO) you cannot solicit things like this that are grammatical rather
than technical.   I think a lot of the developers are also in the same boat
as you (sometimes) try to re-define things that are common language (even
if not accurate technically).

eg - your definition if interlaced versus interweaved..  No matter if you
are right or wrong, the concept and understanding of a majority will
prevail - no exceptions.

Please (for me at least) keep your posts here related to ffmpeg and not
trying to change the nomenclature of what exists.  We are all using the
same software, so whatever the software uses for terminology (as this list
is exactly related to), please do not interfere with that.

Take that up directly with developers and let them sort it out.

On a side note - I have yet seen one of your definitions of a technology
been held up when a developer chimes in - no hard feelings, just that
industry terminology is hard to trump :)

-Greg
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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
On 10/01/2020 12:16 PM, Greg Oliver wrote:
> On Wed, Sep 30, 2020 at 6:25 PM Mark Filipak (ffmpeg) <[hidden email]>
> wrote:
-snip-
> Mark,
>
> Normally I would absolutely defend your queries as they are technical and
> lower level, but I would almost have to side with Bouke from post
> (
> bwdif filter question
> )
>
> You are trying to get free editing for your book now.

I have no book. I intend to have no book. I'm a retired engineer and don't need book proceeds. I
intend to give everything to the ffmpeg project (and anyone else who finds it useful) for free and
unconditionally. It is all public domain. By simply posting it, I'm making it all public domain.

>  I do not agree with
> that..  There are many good contributors and inquisitors (you included),
> but (IMHO) you cannot solicit things like this that are grammatical rather
> than technical.   I think a lot of the developers are also in the same boat
> as you (sometimes) try to re-define things that are common language (even
> if not accurate technically).

I'm working on a glossary, not a dictionary. I have no desire to re-define common language.

> eg - your definition if interlaced versus interweaved..  No matter if you
> are right or wrong, the concept and understanding of a majority will
> prevail - no exceptions.

We shall see, eh? If there's power in (better?) terms, then they will prevail. If not, then they
will die. For what it's worth, I've never written the word "interweaved".

Certainly, to cite just one realm, the current nomenclature is quite confused regarding pre-decoding
streams v. post-decoding processing. The H.xxx folks leave interpretation to "context". But relying
on context relies on understanding, and it is understanding that is lacking. Which would you shoot
first? The chicken or the egg? -- Buy this concept or I shoot the dog.

> Please (for me at least) keep your posts here related to ffmpeg and not
> trying to change the nomenclature of what exists.  We are all using the
> same software, so whatever the software uses for terminology (as this list
> is exactly related to), please do not interfere with that.

My experience is that the entire video field, not just ffmpeg, is grossly underspecified. That hurts
users and developers -- a lot of time is wasted and a lot of feelings are hurt. Based on my 47 years
of engineering experience, the first things that need to be fixed is to unequivocally and
unambiguously define all the terms & structures. To me, that's the low hanging fruit. Then comes the
processes, but once the terms & structures are nailed down, I think we'll all discover that
documenting the processes will be a snap.

> Take that up directly with developers and let them sort it out.

I would/could never stop them from contributing. But it should be acknowledged that the developers
have a developer's perspective. The developer view is like looking out at the world through a pinhole.

> On a side note - I have yet seen one of your definitions of a technology
> been held up when a developer chimes in - no hard feelings, just that
> industry terminology is hard to trump :)

Oh, believe me, you've seen nothing yet. I ponder terminology and anguish over every word choice for
a long, long time. I doggedly seek to manufacture terms that are intuitive and acceptable to all.

The developers have their opinions and have not been shy sharing it. To be honest, I don't see how
this (my glossary) can even be an issue. I'm an ffmpeg user and so long as I'm courteous and focus
on video issues, the developers should welcome me. If not, then I should be removed from the
ffmpeg-user list.

Give this journey the time that it deserves. We all have the same destination in sight, just
differing paths to get there. Perhaps there exists no single path, eh?

--
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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Re: Glossary: Nyquist

Anatoly
In reply to this post by Mark Filipak (ffmpeg)
On Wed, 30 Sep 2020 19:21:59 -0400
"Mark Filipak (ffmpeg)" <[hidden email]> 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.

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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
On 10/01/2020 07:43 PM, Anatoly wrote:

> On Wed, 30 Sep 2020 19:21:59 -0400
> "Mark Filipak (ffmpeg)" <[hidden email]> 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.

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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African-Americans wake up in a police state every day.
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Re: Glossary: Nyquist

Anatoly
On Thu, 1 Oct 2020 20:25:30 -0400
"Mark Filipak (ffmpeg)" <[hidden email]> wrote:

> On 10/01/2020 07:43 PM, Anatoly wrote:
> > On Wed, 30 Sep 2020 19:21:59 -0400
> > "Mark Filipak (ffmpeg)" <[hidden email]> 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.
>
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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Re: Glossary: Nyquist

Eduardo Alarcón
El vie., 2 oct. 2020 a las 7:34, Anatoly (<[hidden email]>)
escribió:

> On Thu, 1 Oct 2020 20:25:30 -0400
> "Mark Filipak (ffmpeg)" <[hidden email]> wrote:
>
> > On 10/01/2020 07:43 PM, Anatoly wrote:
> > > On Wed, 30 Sep 2020 19:21:59 -0400
> > > "Mark Filipak (ffmpeg)" <[hidden email]> 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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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
In reply to this post by Anatoly
On 10/02/2020 06:34 AM, Anatoly wrote:

> On Thu, 1 Oct 2020 20:25:30 -0400
> "Mark Filipak (ffmpeg)" <[hidden email]> wrote:
>> On 10/01/2020 07:43 PM, Anatoly wrote:
>>> On Wed, 30 Sep 2020 19:21:59 -0400
>>> "Mark Filipak (ffmpeg)" <[hidden email]> 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.
>>
> So you want to say that if I watching picture on 640x480 dots
> display, my brain "effectively" can percept only 320x240 dots.

Hi Anatoly,

The issue is not biology, The issue is pure physics.

In your scenario, your eyes do see 640x480. Your brain does see 640x480. But in order to cleanly
'see' a black-white edge inside those 640x480 dots, the 640x480 dots need to be made from 1280x960
samples within the camera. If the camera made 640x480, then, yes, you would see that edge at 320x240
effective resolution (i.e. fuzzier).

I'm trying to prepare some illustrations that will show how Nyquist works in images. That's proving
to be really hard. Two-dimensional Nyquist is hard to visualize.

In the mean time, and in answer to your's & Eduardo's posts, I'm going to write an explanation
instead of showing an explanation.

The Nyquist criterion is based on physics not biology. In physics, perceiving/measuring physical
properties is based on moving energy from object to observer plus the time that takes. If energy
doesn't move, then there is no measurement or observable result.

The interpretation of Nyquist at Wikipedia addresses 1-dimensional voltage (a signal). What is
presented is limited to one dimension plus time.

However, over a 2-dimensional area (such as a display), the more general interpretation of
resolution is based on the rate of change of energy density per unit of time. Higher energy (e.g.
more light) makes images more resolvable. Higher density (e.g. more dots per square mm) makes images
more resolvable. More time (e.g. longer observation) makes images more resolvable.

Anyone who thinks that Nyquist sampling is limited to signals is wrong. Nyquist sampling applies to
2-dimensional areas, too. (Nyquist applies to 3-dimensions, also, but that's another story.)

Nyquist applies to anything/everything that's converted from analog to digital.

> 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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> https://ffmpeg.org/mailman/listinfo/ffmpeg-user
>
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> [hidden email] with subject "unsubscribe".
>


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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
In reply to this post by Eduardo Alarcón
On 10/02/2020 02:15 PM, Eduardo Alarcón wrote:

> El vie., 2 oct. 2020 a las 7:34, Anatoly (<[hidden email]>)
> escribió:
>
>> On Thu, 1 Oct 2020 20:25:30 -0400
>> "Mark Filipak (ffmpeg)" <[hidden email]> wrote:
>>> 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, ...

Not correct. It's not biological, but it does apply to biology, specifically, to the eyes.

Okay, 2 thought experiments:
1 - Imagine a film scanner sampling a film frame line by line. Isn't the scanner making a signal
that the sampler uses to make samples? If you think that Nyquist applies only to signals, then,
there's your signal.
2 - What about a CCD array that makes all the samples at one time? Doesn't that expand the signal to
2 dimensions?

>... it describes the minimum sampling rate ...

Nyquist has nothing to do with rate. If Wikipedia says otherwise, then Wikipedia is wrong. Rate only
applies to broadcast media like television. Rate determines bandwidth needed (which may be more than
what's allowed for channels), but bandwidth is meaningless in a film scanner or a camera because
they are not broadcast.

What Wikipedia may be referring to is the bandwidth needed for digital TV. That really has nothing
to do with Nyquist. But then, Wikipedia isn't written by experts, is it? I can see how it would
mislead you.

By the way, I've given up trying to make an illustration of 2-dimensional Nyquist sampling. It's too
hard.

--
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Re: Glossary: Nyquist

Anatoly
On Fri, 2 Oct 2020 20:47:57 -0400
"Mark Filipak (ffmpeg)" <[hidden email]> wrote:

>In your scenario, your eyes do see 640x480. Your brain does see
>640x480. But in order to cleanly 'see' a black-white edge inside those
>640x480 dots, the 640x480 dots need to be made from 1280x960 samples
>within the camera. If the camera made 640x480, then, yes, you would see
>that edge at 320x240 effective resolution (i.e. fuzzier).
I may not agree with it. What is algorithm to downsample from 1280 to
640 do you propose? How it will differ from natural optical process
of splitting one white dot of projected on CCD image into two CCD
pixels sampled values?
-snip-  
> Okay, 2 thought experiments:
> 1 - Imagine a film scanner sampling a film frame line by line. Isn't
> the scanner making a signal that the sampler uses to make samples? If
> you think that Nyquist applies only to signals, then, there's your
> signal. 2 - What about a CCD array that makes all the samples at one
> time? Doesn't that expand the signal to 2 dimensions?
Then I guessed you want to say different thing:
In order to reproduce image of 640 black-white alternating vertical
stripes *guaranteed clarly, without possible interference*, we need
horizontal resolution from CCD to LCD of 1280.
This is true, but there is nothing to deal with Nyquist criteria as it
is trivial to all technicians that Nyquist determinies *minimum*
necessary sampling rate (temporal or spatial if you wish) to
have possibility to reproduce given oroginal.
Same thing with sound, for ex. 44100Hz sampling rate is minimal
requirement to digitize 22050Hz wave, but quality of that digitized wave
will be low, you easily can get interference with sampling freqency.
But al least you can do it, because it satisfy Nyquist criteria.

> >... it describes the minimum sampling rate ...
Yes it is.  
>
> Nyquist has nothing to do with rate.
Temporal rate in analogue video signal is just another representation of
spatial rate of CCD pixels.

> By the way, I've given up trying to make an illustration of
> 2-dimensional Nyquist sampling. It's too hard.
I think is's easy. Just slale dows to every one dimesion to tart from.
Lets draw XY plot of one line of our picture of alternating black-white
stripes

Voltage     ^
  -or-      |
Light       |
intencity   | b    w    b    w
            |     ___       ___
            |    /   \     /   \
            |___/     \___/     \_
            |_______________________> Time -or- position

            --|----|----|----|--- samples

              _    _    _    _
             / \__/ \__/ \__/ \_  sampling freq -or- distance.

Here we are digitizing 4 pixels. Does not matter how they are separated
one from another - temporarily (analogue video signal) or spatialy
(laying on CCD silicone surface). Nyquist criteria says that to
digitize (somehow) 4 pixels we need to take 4 samples. Note that
our "signal" frequency (again, temporal or spatial) is 1/2 of sampling
frequency. That is it.
Maybe it's a fun to discuss such a things, but I think here is not
right place to do it, beacuse it has no straight relation to ffmpeg
usage.
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Re: Glossary: Nyquist

Mark Filipak (ffmpeg)
On 10/03/2020 06:41 AM, Anatoly wrote:
> On Fri, 2 Oct 2020 20:47:57 -0400
> "Mark Filipak (ffmpeg)" <[hidden email]> wrote:
-snip-

>> By the way, I've given up trying to make an illustration of
>> 2-dimensional Nyquist sampling. It's too hard.
> I think is's easy. Just slale dows to every one dimesion to tart from.
> Lets draw XY plot of one line of our picture of alternating black-white
> stripes
>
> Voltage     ^
>    -or-      |
> Light       |
> intencity   | b    w    b    w
>              |     ___       ___
>              |    /   \     /   \
>              |___/     \___/     \_
>              |_______________________> Time -or- position
>
>              --|----|----|----|--- samples
>
>                _    _    _    _
>               / \__/ \__/ \__/ \_  sampling freq -or- distance.
>
> Here we are digitizing 4 pixels. Does not matter how they are separated
> one from another - temporarily (analogue video signal) or spatialy
> (laying on CCD silicone surface). Nyquist criteria says that to
> digitize (somehow) 4 pixels we need to take 4 samples. Note that
> our "signal" frequency (again, temporal or spatial) is 1/2 of sampling
> frequency. That is it.

Where's the twice the display resolution in your diagram?

My understanding of Nyquist is limited. I think that it's based on the information density present
in a signal having amplitude S, that transitions from S to S+d(S) (not black to white) and that it
therefore defines a minimal slope (hence, the connection to bandwidth). I, myself, question that
bandwidth is an adequate metric and whether 'information' is adequately characterized, but science
only 'sees' what it can measure, eh? I'll stick with a definition based on energy density (which, in
the listening and the seeing, has a gaussian profile and is based on physics).

> Maybe it's a fun to discuss such a things, but I think here is not
> right place to do it, beacuse it has no straight relation to ffmpeg
> usage.

If not ffmpeg.org, then where? doom9.org? -- no organization there, a glossary would get lost. Or
Wikipedia? Ha!

The audience is here. ...Perhaps Wikipedia some day.

--
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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Re: Glossary: Nyquist

Anatoly
On Sat, 3 Oct 2020 11:05:03 -0400
"Mark Filipak (ffmpeg)" <[hidden email]> wrote:

> On 10/03/2020 06:41 AM, Anatoly wrote:
> > On Fri, 2 Oct 2020 20:47:57 -0400
> > "Mark Filipak (ffmpeg)" <[hidden email]> wrote:  
> -snip-
> >> By the way, I've given up trying to make an illustration of
> >> 2-dimensional Nyquist sampling. It's too hard.  
> > I think is's easy. Just slale dows to every one dimesion to tart
> > from. Lets draw XY plot of one line of our picture of alternating
> > black-white stripes
> >
> > Voltage     ^
> >    -or-      |
> > Light       |
> > intencity   | b    w    b    w
> >              |     ___       ___
> >              |    /   \     /   \
> >              |___/     \___/     \_  
> >              |_______________________> Time -or- position  
> >
> >              --|----|----|----|--- samples
> >
> >                _    _    _    _
> >               / \__/ \__/ \__/ \_  sampling freq -or- distance.
> >
> > Here we are digitizing 4 pixels. Does not matter how they are
> > separated one from another - temporarily (analogue video signal) or
> > spatialy (laying on CCD silicone surface). Nyquist criteria says
> > that to digitize (somehow) 4 pixels we need to take 4 samples. Note
> > that our "signal" frequency (again, temporal or spatial) is 1/2 of
> > sampling frequency. That is it.  
>
> Where's the twice the display resolution in your diagram?
What twice resolution? Please re-read my letter carefully (text above).
Do you see "Voltage -or- Light intencity" wave? It has frequency "B"
Do you see "sampling freq. -or- distance" wave? It has frequency 2B
To digitize (somehow, not at it's best) wave that has frequency B, we
need samplerate 2B. That's all. No matter if "frequency" is spatial or
temporal, it's just a X-Y function plot.

>
> My understanding of Nyquist is limited. I think that it's based on
> the information density present in a signal having amplitude S, that
> transitions from S to S+d(S) (not black to white) and that it
> therefore defines a minimal slope (hence, the connection to
> bandwidth). I, myself, question that bandwidth is an adequate metric
> and whether 'information' is adequately characterized, but science
> only 'sees' what it can measure, eh? I'll stick with a definition
> based on energy density (which, in the listening and the seeing, has
> a gaussian profile and is based on physics).
You should learn than what spectrum is. And how any complex waveform
(with it's "information density") may be represented as a sum of many
simple sinewaves.
Then you'll understand that all that may be simplified to the
picture I draw, and to that the definition of Nyquist-Shannon theorem
literally states (again):
"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."

>
> > Maybe it's a fun to discuss such a things, but I think here is not
> > right place to do it, beacuse it has no straight relation to ffmpeg
> > usage.  
>
> If not ffmpeg.org, then where? doom9.org? -- no organization there, a
> glossary would get lost. Or Wikipedia? Ha!
I really don't know. Maybe because of my prsonal approach that is to
create my own resources for my own projects, then just link to it.
> The audience is here. ...Perhaps Wikipedia some day.
>
Then I may wish you to show worthy draft of your project to audience
before the audience gets completely bored. Good luck!

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