How "reliable" is this school tutorial page on sampling?

Hello,

I am following closely the current UK mailing lists etc concerned with 
teaching Computing at school level, it having never previously been a 
part of the curriculum. The UK government has  asked everyone to teach 
computer science starting this September. New exam curricula are popping 
up all over the place, and new tutorial resources etc. There is a 
certain amount of panic amongst many teachers who have never taught 
programming and CS before; and who may be far from conversant with 
digital audio issues. The curriculum includes a minor section on sound, 
almost entirely focussing on the sampling process as an aspect of the 
topic "data representation". This may be the only way digital audio gets 
into the core school curriculum, so it is important that even if to a 
degree dumbed down it presents the topics as correctly as is reasonable 
at that level, in a way that can be built upon.

A representative public tutorial page is this (very long URL):

http://en.wikibooks.org/wiki/A-level_Computing/AQA/Problem_Solving,_Programming,_Data_Representation_and_Practical_Exercise/Fundamentals_of_Data_Representation/Sampled_sound

This page targets UK "A-Level" students, i.e. pre-university, 16-18 age 
group.

Now, setting aside the often awkward and strangely non-technical 
language, my question is: am I wrong to think that this over-argues the 
idea that prefect reconstruction is impossible?

For example, it presents the quasi exam question "Why can't a digital 
representation of a sound ever be a perfect representation?", with the 
ostensibly definitive answer "A sound wave is continuous data, whilst 
digital data is discrete".

I am well aware that the sampling theorem describes an "ideal" situation 
that cannot be fully realised in a practical system, but is this page 
nevertheless OTT, or worse?

Richard Dobson

>For example, it presents the quasi exam question "Why can't a digital 
>representation of a sound ever be a perfect representation?", with the 
>ostensibly definitive answer "A sound wave is continuous data, whilst 
>digital data is discrete".

I would say for digital data, the amplitude has been quantized as the
reason there can never be perfect representation. There's discrete time
(sampling) and discrete amplitude (quantization). To say that digital data
is discrete is not specific enough.

The answer to the last question should include the word "stereo."

On Mon, 18 Jun 2012 21:44:22 +0100, Richard Dobson wrote:

> Hello,
> 
> I am following closely the current UK mailing lists etc concerned with
> teaching Computing at school level, it having never previously been a
> part of the curriculum. The UK government has  asked everyone to teach
> computer science starting this September. New exam curricula are popping
> up all over the place, and new tutorial resources etc. There is a
> certain amount of panic amongst many teachers who have never taught
> programming and CS before; and who may be far from conversant with
> digital audio issues. The curriculum includes a minor section on sound,
> almost entirely focussing on the sampling process as an aspect of the
> topic "data representation". This may be the only way digital audio gets
> into the core school curriculum, so it is important that even if to a
> degree dumbed down it presents the topics as correctly as is reasonable
> at that level, in a way that can be built upon.
> 
> A representative public tutorial page is this (very long URL):
> 
> http://en.wikibooks.org/wiki/A-level_Computing/AQA/
Problem_Solving,_Programming,_Data_Representation_and_Practical_Exercise/
Fundamentals_of_Data_Representation/Sampled_sound
> 
> This page targets UK "A-Level" students, i.e. pre-university, 16-18 age
> group.
> 
> Now, setting aside the often awkward and strangely non-technical
> language, my question is: am I wrong to think that this over-argues the
> idea that prefect reconstruction is impossible?
> 
> For example, it presents the quasi exam question "Why can't a digital
> representation of a sound ever be a perfect representation?", with the
> ostensibly definitive answer "A sound wave is continuous data, whilst
> digital data is discrete".
> 
> I am well aware that the sampling theorem describes an "ideal" situation
> that cannot be fully realised in a practical system, but is this page
> nevertheless OTT, or worse?

Well, the example question and answer you give is similar to "Why does 
gravity work?", with the ostensibly definitive answer "because when I 
drop something, it hits the floor".  Of course, "Because God said so" has 
the advantage of being just as correct as either their answer to their 
question or my answer to mine while being universally applicable, but I 
suppose that universal applicability doesn't overcome it's essential 
meaninglessness in scientific terms.

The rest of the questions and answers are good as far as they go, and 
frankly, it's hard for university graduates with degrees in electrical 
engineering to understand the nuances of sampling.  So veiling "because 
God said so" behind one thin layer of rhetoric is certainly tempting.

If you want to explain the Nyquist criterion then you have to explain the 
notion of a frequency spectrum; then you get all snarled up in the notion 
of power spectral _density_, where a signal doesn't have any energy AT 
ALL right at 1kHz, but if you average the power over the span of 1Hz 
_around_ 1kHz then there's real power, etc.

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

On Mon, 18 Jun 2012 21:44:22 +0100, Richard Dobson
<richarddobson@blueyonder.co.uk> wrote:

>Hello,
>
>I am following closely the current UK mailing lists etc concerned with 
>teaching Computing at school level, it having never previously been a 
>part of the curriculum. The UK government has  asked everyone to teach 
>computer science starting this September. New exam curricula are popping 
>up all over the place, and new tutorial resources etc. There is a 
>certain amount of panic amongst many teachers who have never taught 
>programming and CS before; and who may be far from conversant with 
>digital audio issues. The curriculum includes a minor section on sound, 
>almost entirely focussing on the sampling process as an aspect of the 
>topic "data representation". This may be the only way digital audio gets 
>into the core school curriculum, so it is important that even if to a 
>degree dumbed down it presents the topics as correctly as is reasonable 
>at that level, in a way that can be built upon.
>
>A representative public tutorial page is this (very long URL):
>
>http://en.wikibooks.org/wiki/A-level_Computing/AQA/Problem_Solving,_Programming,_Data_Representation_and_Practical_Exercise/Fundamentals_of_Data_Representation/Sampled_sound
>
>This page targets UK "A-Level" students, i.e. pre-university, 16-18 age 
>group.
>
>Now, setting aside the often awkward and strangely non-technical 
>language, my question is: am I wrong to think that this over-argues the 
>idea that prefect reconstruction is impossible?
>
>For example, it presents the quasi exam question "Why can't a digital 
>representation of a sound ever be a perfect representation?", with the 
>ostensibly definitive answer "A sound wave is continuous data, whilst 
>digital data is discrete".

That sounds like the sort of answer I'd expect from somebody who
thinks that vinyl reproduces music better than a CD, and there are
certainly a lot of people who think that.

I don't think they're right, but, hey...

>I am well aware that the sampling theorem describes an "ideal" situation 
>that cannot be fully realised in a practical system, but is this page 
>nevertheless OTT, or worse?

I think that particular suggested answer is not good and probably
misleading if one is trying to teach sampling theory.


Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com

David Drumm <drumm@n_o_s_p_a_m.coherentlogix.com> wrote:
>>For example, it presents the quasi exam question "Why can't a digital 
>>representation of a sound ever be a perfect representation?", with the 
>>ostensibly definitive answer "A sound wave is continuous data, whilst 
>>digital data is discrete".

> I would say for digital data, the amplitude has been quantized as the
> reason there can never be perfect representation. There's discrete time
> (sampling) and discrete amplitude (quantization). To say that digital data
> is discrete is not specific enough.

Sound waves are not continuous, as air is made of discrete molecules,
which bounce around, such as off your eardrum.

There are systems that store sampled voltage on capacitors,
so only quantized to the whole numbers of electrons on the
capacitor plates. If you get a good enough A/D converter, you
should be able to quantize down to the molecular limit.
What does it have to do to be perfect?

> The answer to the last question should include the word "stereo."

-- glen

From David Drumm:
>For example, it presents the quasi exam question "Why can't a digital 
>representation of a sound ever be a perfect representation?"

From glen herrmannsfeldt:
> Sound waves are not continuous, as air is made of discrete molecules,
> which bounce around, such as off your eardrum.

The answer was actually sitting right in the middle of the final comment made by the original poster. You only got half of it -- a sound wave, when thought of as a function of time, is/is not such and such. But the REAL issue is not what the sound wave looks like, in terms of its temporal variation, but in terms of its SPATIAL distribution at EACH time.

glen:
> What does it have to do to be perfect?

David:
> The answer to the last question should include the word "stereo."

It has to be holophonic, rather than stereophonic. The same thing goes for images. A stereo image in a 3-D movie only shows you the 3-D perspective from one vantage point. A holographic reproduction shows you 3-dimensionality *independent* of where you are sitting when you look at the image.

In a holophonic reproduction, for instance, the sound of foot steps going across an imaginary table in the middle of the room will be heard as moving across the room no matter where you sit when you listen to it, and it will be heard as coming from the "table" sitting at that one spot, even as you move around the location of the imaginary table.

I posted some of the math needed to do find the best-fitting speaker output for a given 3-D waveform here. That's statistically optimal holophony -- a compromise between true honest-to-goodness holophonic reproduction and stereophonic reproduction

2012 June 1: Equations for Holophony, sci.physics.research
https://groups.google.com:443/forum/?fromgroups#!search/sci.physics.research/sci.physics.research/Hn6ecH09OkM/UTObFLUm6voJ

The Wikipedia article referenced therein has more information and has a bibliography and links to PDF's from the research literature.

I do not know what least squares fit will produce, in terms of quality, if the speakers a few in number (like only 10 or 20) and separated by feet, rather than mere inches. I only know it's going to be better than stereo. My math, BTW, is generic, to 2-D level playing fields as well as 3-D arenas. The research literature, for some reason, generally only limits to 2-D fields. The WIkipedia article says there are holophonic systems currently in use, with 2008 being the start date of one such system.

On 19/06/2012 00:38, glen herrmannsfeldt wrote:
..
>
> Sound waves are not continuous, as air is made of discrete molecules,
> which bounce around, such as off your eardrum.
>
> There are systems that store sampled voltage on capacitors,
> so only quantized to the whole numbers of electrons on the
> capacitor plates. If you get a good enough A/D converter, you
> should be able to quantize down to the molecular limit.
> What does it have to do to be perfect?
>

Thank you (and thank you to all those who responded); that fits well 
with an angle I have been considering, that by over-arguing the 
imperfectness of sampling, without any broader context, they are (among 
other things) missing an opportunity to discuss error margins in a more 
general way, both with specific regard to sound quality (the topic 
mandated by the exam specifications) and to issues in numeric computing, 
n'stuff. That is an approach I can make on the main computing education 
mailing list, rather than diving in peremptorily to edit the wiki pages, 
or simply grumbling that it is all "wrong" (and badly written).

Richard Dobson

>> terms of its SPATIAL distribution at EACH time

maybe this is OT, but it's the reason why I still lug a Leslie cabinet
around when gigging. There is no way you could get the sound of a
mechanically rotating, directional horn with fixed speakers. 

mnentwig wrote:
>>> terms of its SPATIAL distribution at EACH time
>
> maybe this is OT, but it's the reason why I still lug a Leslie cabinet
> around when gigging. There is no way you could get the sound of a
> mechanically rotating, directional horn with fixed speakers.
>


http://www.kvraudio.com/product/leslie_by_mda

Doesn't do you much good for live.

--
Les Cargill

yes, that's the point. 
I'm just saying that the difference can be heard easily, not that it makes
much sense otherwise, except maybe as a weight lifting exercise...