[[email protected]]

For some years now the Nyquist Sampling Theorem has been bugging me
and I've decided to come public because none of what I've read
adresses my concern - not directly anyway.

As you all know, the Nyquist theorem states that "Exact
reconstruction of a continuous-time baseband signal from its samples
is possible if the signal is bandlimited and the sampling frequency is
greater than twice the signal bandwidth".

Now if I sample a 1 Hz waveform with a sampling rate of just over 40
kHz then I'd expect to see just over 40 thousand samples for that
single-cycle wave - 20 thousand samples for the positive half and
another 20 thousand for the negative half.

Now go right up to 20 kHz. I get ONE sample in the positive half and
ONE sample in the negative half! That's not too impressive is it? Just
how are you going to reconstruct a 20 kHz wave accurately with just
one sample per half-cycle. That sample could have landed anywhere on
the sine-curve - so how do you know what the maximum amplitude of that
20 kHz wave is?

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

[Don Pearce]

On 2 May 2007 07:58:16 -0700, wrote:

For some years now the Nyquist Sampling Theorem has been bugging me
and I've decided to come public because none of what I've read
adresses my concern - not directly anyway.

As you all know, the Nyquist theorem states that "Exact
reconstruction of a continuous-time baseband signal from its samples
is possible if the signal is bandlimited and the sampling frequency is
greater than twice the signal bandwidth".

Now if I sample a 1 Hz waveform with a sampling rate of just over 40
kHz then I'd expect to see just over 40 thousand samples for that
single-cycle wave - 20 thousand samples for the positive half and
another 20 thousand for the negative half.

Now go right up to 20 kHz. I get ONE sample in the positive half and
ONE sample in the negative half! That's not too impressive is it? Just
how are you going to reconstruct a 20 kHz wave accurately with just
one sample per half-cycle. That sample could have landed anywhere on
the sine-curve - so how do you know what the maximum amplitude of that
20 kHz wave is?

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

No, you can't do it with just those two samples in a 20kHz wave, but
provided you have *more* than two samples, you will find that there is
just one unique sine wave that can be drawn through those
two-and-a-bit samples. That is what the reconstruction filter does. It
all gets much tougher to do as you get closer to the Nyquist rate, of
course.

It will be a sine wave, of course, because there is no possibility of
harmonics. And of course if you do the maths, you find that the
simultaneous presence of other signals is no problem.

d

--
Pearce Consulting
http://www.pearce.uk.com

[Randy Yates]

writes:
[...]

For some years now the Nyquist Sampling Theorem has been bugging me
and I've decided to come public because none of what I've read
adresses my concern - not directly anyway.

As you all know, the Nyquist theorem states that "Exact
reconstruction of a continuous-time baseband signal from its samples
is possible if the signal is bandlimited and the sampling frequency is
greater than twice the signal bandwidth".

This is correct. Note the term "greater than."

Now go right up to 20 kHz.

Then the sampling rate isn't "greater than."

There is nothing else wrong in your reasoning.
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

[[email protected]]

Then the sampling rate isn't "greater than."

Point taken Randy. I was aware of this when I wrote it but stopped
myself saying "just greater than" to keep things simple.

Glad to hear you think the reasoning is correct though! I wonder what
others will think?

Eddy

[Randy Yates]

writes:

Then the sampling rate isn't "greater than."

Point taken Randy. I was aware of this when I wrote it but stopped
myself saying "just greater than" to keep things simple.

Glad to hear you think the reasoning is correct though! I wonder what
others will think?

You're welcome, Eddy.

However, what others think is irrelevent. It can be shown
mathematically to be so.

Chris Bores probably has something about this on his web site on DSP
tutorials. Google for him.
--
% Randy Yates % "Midnight, on the water...
%% Fuquay-Varina, NC % I saw... the ocean's daughter."
%%% 919-577-9882 % 'Can't Get It Out Of My Head'
%%%% % *El Dorado*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

[Norbert Hahn]

wrote:

Now go right up to 20 kHz. I get ONE sample in the positive half and
ONE sample in the negative half! That's not too impressive is it?

That just wrong. If you look at your 20 kHz wave for one second
you get 40.001 or more samples and you're able to reconstruct
the original wave. The shorter the time you use to look at the
wave the more errors you get. If you restrict yourself to only
two samples your bandwidth is no longer deliminted to fs/2.

Norbert

[GregS]

In article .com, wrote:
For some years now the Nyquist Sampling Theorem has been bugging me
and I've decided to come public because none of what I've read
adresses my concern - not directly anyway.

But its always interesting Nyquist was working with pulses, not waves.
I think the correct issue is the Sampling Theorem by Shannon.

greg

[Randy Yates]

writes:
[...]
Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Eddy,

I retract my initial response to you - sorry for the confusion! I didn't
read all the way through your post.

It is helpful to separate theory from practice in issues like these.

In theory, you can reconstruct ANY frequency between 0 = f Fs/2. Notice
the inequalities - they are important. In theory, you CANNOT reconstruct
(in general) a frequency AT Fs/2.

In practice, the computational complexity gets higher the closer you
want to come to Fs/2. However, even in practice, it is not unreasonable
to expect to get to within 80 percent of Fs/2 or even closer. I recently
designed a filter (it was a monster, though) that was down 80 dB at within
95 percent of Nyquist.

So, no, you can't get exactly TO Fs/2, even theoretically, but also no,
you don't have to have 4 or 5 samples per cycle.

As far as I'm concerned, the high sample rate stuff (DSD, DVD-A, etc.) is
BS.
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

[John Phillips]

On 2007-05-02,
wrote:
For some years now the Nyquist Sampling Theorem has been bugging me
...
As you all know, the Nyquist theorem states that "Exact
reconstruction of a continuous-time baseband signal from its samples
is possible if the signal is bandlimited and the sampling frequency is
greater than twice the signal bandwidth".

Now if I sample a 1 Hz waveform with a sampling rate of just over 40
kHz then I'd expect to see just over 40 thousand samples for that
single-cycle wave - 20 thousand samples for the positive half and
another 20 thousand for the negative half.

Now go right up to 20 kHz. I get ONE sample in the positive half and
ONE sample in the negative half! That's not too impressive is it? Just
how are you going to reconstruct a 20 kHz wave accurately with just
one sample per half-cycle. That sample could have landed anywhere on
the sine-curve - so how do you know what the maximum amplitude of that
20 kHz wave is?

To know the amplitude you need to limit the signal to *just below* 20 kHz.
20 kHz is aliased to 0 Hz if sampled at 40 ksamples/s.

Then the point is that if you draw ANY line (yes, ANY) through the 2+
samples per cycle then the theorem's corrolory is that the resulting
reconstructed signal is the original waveform *precisely*, plus another
signal whose spectral components are ALL above 20 kHz (the Nyquist limit).
So you "just" need to filter that out to get the original back perfectly.

Of course that may be a difficult engineering job so it is usual to
leave some space between the maximum wanted frequency (say 20 kHz)
and the Nyquist limit at half the sample rate (say 22.05 ksamples/s).
Also it is useful to re-construct the signal with a fairly intelligently
drawn line to limit the amplitude of the unwanted spectral images above
the Nyquist limit (so that filtering is again easier).

The bigger the space the easier it is to:

- bandlimit the original signal before the A/D without any significant
(i.e. audible) amplitude or phase damage to the original; and

- filter out the spectral images above the Nyquist limit without
any amplitude or phase damage to the re-constructed signal.

So yes - having more samples per cycle makes the *engineering* easier
but the theory is good right up to 2+delta samples per cycle (for delta
as small as you like but not zero).
--
John Phillips

[Steven Sullivan]

Soundhaspriority wrote:

wrote in message
oups.com...
[snip]

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

You will probably find this ignites a "flame war", but stick to your
guns. You're right.

As I understand it, this is not a problem if oversampling is used. And if it isn't (rare
nowadays), it's not a problem *if* the player's filters are well-implemented, in which case
the phase shift should be practically inaudible. The technical difficulty/cost-effectiveness
of implementing such filtering is the reason why oversampling has been the norm for years now
in CD players.


___
-S
"As human beings, we understand the world through simile, analogy,
metaphor, narrative and, sometimes, claymation." - B. Mason

[[email protected]]

On May 2, 10:58 am, wrote:

As you all know, the Nyquist theorem states that "Exact
reconstruction of a continuous-time baseband signal from its samples
is possible if the signal is bandlimited and the sampling frequency is
greater than twice the signal bandwidth".

Now if I sample a 1 Hz waveform with a sampling rate of just over 40
kHz then I'd expect to see just over 40 thousand samples for that
single-cycle wave - 20 thousand samples for the positive half and
another 20 thousand for the negative half.

Now go right up to 20 kHz. I get ONE sample in the positive half and
ONE sample in the negative half! That's not too impressive is it? Just
how are you going to reconstruct a 20 kHz wave accurately with just
one sample per half-cycle. That sample could have landed anywhere on
the sine-curve - so how do you know what the maximum amplitude of that
20 kHz wave is?

But you just violated the Nyquist criteria by having the
sample rate be EXACTLY twice the frequency of interest:
your example is broken.

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

Nope, your understanding is faulty.

The sampling theorem works because even though there
an infinite number of waveforms that can pass through
those points, ONE AND ONLY ONE meets the important
critera that it's total energy is limited to less than 1/2 the
sampling rate.

Let's take a somewhete easier example: a 10 kHz sine
wave sampled at 40 kHz. that gives 4 points per 10 kHz
cycle. But not only will that 10 kHz sine wave fully match
all the samples, but so will a30 khz sine wave of the same
amplitude, a 50 Khz, 70 Kz, 90 kHz and so on to infinity.
In fact, one can imaging a non-sinusoidal waveform that
passes precisely through every one of the samples.

So why does ONLY the EXACT 10 kHz sine wave that
went in also come out?

Because that's the ONLY one of the infinite number of
possible waveforms that has those particular sample
values AND falls within the 20kHz Nyquist bandwidth.
All others are eliminated in the reconstruction/anti-
imaging filter. IN the case out our complicated non-sinu-
soidal waveform, it consitis of a 10 kHz waveform plus
lots of hamronics, all of which fall outside of the bandwidth
of the system.

All those the "images" of the original 10 kHz wave,
the ones that can also be desccribed by the sample
stream, are all present, all the way up to infinity, in
the sample digital stream The original 0-20 kHz
base band has an image (frequency inverted) from
20-40 kHz, another (non-inverted) from 40-60 kHz,
another inverted one from 60-80 kHz, ad infinitum.

ALL of them are present in a discrete time-sampled
stream. Any one of them can be considered "valid,"
and, in fact, represent a means of shifting the signal
in frequency.

But the ENTIRE point in the anti-imaging filter is to
filter out all the "images" that aren't wanted. and to
leave the one that is, in this case, the baseband
(0-20 kHz).

(In fact, if you were to sum ALL the possible waves
that could pass through the samples, you'd end up
with a train of infinitely narrow pulses: the amplitude
of the stream would be exactly 0 between samples,
and it would rise or fall in zero time to the sample
value. Such a waveform, if you were to look at its
frequency content, would have harmonics extending
out to infinity, filter out ALL of the harmonics of a
complex waveform, leaving only the fundamental,
and, poof, out comes only a sine wave)

This seems to argue for a sampling rate of 4 or 5
times the Nyquist minimum limit.

Nope,, it argues that your model is wrong, and that
you're leaving out the imaging and required image
filtering portion of the system.

Perhaps this is why DVD sampling is at 192 kHz?

Nope, it's because it can, and thuc can sell. There is
no justification technically for it along the lines you
are considering.

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

In summary, then, you have two flaws:

1. The first, a somewhat minor on, but one that trips
most people up, is that you gave an example where
you are sampling at EXACTLY twice the frequency of
interest,

2. The second, and the one that is most fundamental, is
that you have neglected the vital stage of the anti-image
and reconstruction fuilter to eliminate the ambiguities in
the stream that you point out. Those ambiguities are,
in fact, the out-of-band images that the anti-imaging filter
eliminates.

[[email protected]]

On May 2, 12:23 pm, "Soundhaspriority" wrote:
wrote in message

oups.com...
[snip]



Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

In a word, bullsh*t.

It does NOT manifest itself as phase shift. Typical phase shift
errorsof a the vast majority of 44.1 kHz sampling systems
are less than a dozen or so degeres right up to cutoff.


If you assertion were correct, the effects you claim would
be trivial to measure. Clearly, you have NOT measured
them becuase, if you had, you would have not been honestly
able to make these claims.

You will probably find this ignites a "flame war", but stick to your
guns. You're right.

No, he's not, he's mistaken. But at least he ASKED the
question instead of spouting nonsense, as you just did.

What ignires flame wars is not honest questions, or even
wrong guesses as the original poster wrote, but uninformed
op9inion pasing as fact, as you just did.

[[email protected]]

Thanks for all your remarkably understanding replies. I have noticed
in the past that sometimes the simplest questions don't get simple
answers.

I can see now that I should have remembered my Fourier analysis. I
don't know how these sine waves are reconstructed but I can see from
your responses that, from the infinite number of possible sine wave
solutions, there is only one solution, provided bandwidth is limited
appropriately.

That answers my original concern - which has been bugging me for some
15 years now. It's nice to have that burden off my shoulders at last!

Cheers

Eddy

[Randy Yates]

"Soundhaspriority" writes:

wrote in message
ups.com...
On May 2, 12:23 pm, "Soundhaspriority" wrote:
wrote in message

oups.com...
[snip]



Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist
limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

In a word, bullsh*t.

It does NOT manifest itself as phase shift. Typical phase shift
errorsof a the vast majority of 44.1 kHz sampling systems
are less than a dozen or so degeres right up to cutoff.

You are WRONG.

I think it depends on the architecture used in the A/D.

If the A/D runs at the final sample rate (e.g., 44.1 kHz), then the
analog filter must be sharp, and there would be significant phase
distortion near Fs/2.

If the A/D oversamples, then the filter requirement is relaxed and
the phase shift may be relatively benign at Fs/2.

I have to admit, as much as I respect Dick, that I must agree with
you, Bob, in this particular context and discussion.

HOWEVER...., the very relevent piece of information that most of the
"high-sample-rate advocates" seem to conveniently omit is that the
high sample rate is only required the data conversion ends of the
chain.

That is, the storage medium can use the "sane" sample rates of
44.1 or 48 kHz while the A/D and D/A end-points do the appropriate
downconversion and upconversion, respectively, that is necessary to
overcome the filtering problems. There is no need for 192 kHz DVD-A.
--
% Randy Yates % "Ticket to the moon, flight leaves here today
%% Fuquay-Varina, NC % from Satellite 2"
%%% 919-577-9882 % 'Ticket To The Moon'
%%%% % *Time*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

[Steven Sullivan]

Soundhaspriority wrote:

"Steven Sullivan" wrote in message
...
Soundhaspriority wrote:

wrote in message
oups.com...
[snip]

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist
limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

You will probably find this ignites a "flame war", but stick to your
guns. You're right.

As I understand it, this is not a problem if oversampling is used. And if
it isn't (rare
nowadays), it's not a problem *if* the player's filters are
well-implemented, in which case
the phase shift should be practically inaudible. The technical
difficulty/cost-effectiveness
of implementing such filtering is the reason why oversampling has been the
norm for years now
in CD players.

It is a problem at some point near the Nyquist frequency.


For 44.1 sampling rate, that's ~22 kHz. Not much of a problem, *really*,
and even the theoreticalally audible issues are addressed by oversampling .

I leave you to Mr.Pierce for the rest of the dissection.



___
-S
"As human beings, we understand the world through simile, analogy,
metaphor, narrative and, sometimes, claymation." - B. Mason

[Don Pearce]

On Wed, 02 May 2007 22:23:08 -0400, Randy Yates
wrote:

"Soundhaspriority" writes:

wrote in message
ups.com...
On May 2, 12:23 pm, "Soundhaspriority" wrote:
wrote in message

oups.com...
[snip]



Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist
limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

In a word, bullsh*t.

It does NOT manifest itself as phase shift. Typical phase shift
errorsof a the vast majority of 44.1 kHz sampling systems
are less than a dozen or so degeres right up to cutoff.

You are WRONG.

I think it depends on the architecture used in the A/D.

If the A/D runs at the final sample rate (e.g., 44.1 kHz), then the
analog filter must be sharp, and there would be significant phase
distortion near Fs/2.

If the A/D oversamples, then the filter requirement is relaxed and
the phase shift may be relatively benign at Fs/2.

I have to admit, as much as I respect Dick, that I must agree with
you, Bob, in this particular context and discussion.

HOWEVER...., the very relevent piece of information that most of the
"high-sample-rate advocates" seem to conveniently omit is that the
high sample rate is only required the data conversion ends of the
chain.

That is, the storage medium can use the "sane" sample rates of
44.1 or 48 kHz while the A/D and D/A end-points do the appropriate
downconversion and upconversion, respectively, that is necessary to
overcome the filtering problems. There is no need for 192 kHz DVD-A.

What do you mean by "if" the A/D oversamples (and I presume you
include the D/A in that). I can't think of a single example of one
that doesn't. As far as I am concerned it is a vital part of the
process.

As far as the real world is concerned, Dick is spot on. I've seen
reconstruction filters that demonstrate virtually no measurable phase
shift at 20kHz.

d

--
Pearce Consulting
http://www.pearce.uk.com

[Arny Krueger]

"Soundhaspriority" wrote in message


wrote in message
oups.com...

Surely you'd need about four or five samples per
half-cycle to even hope to reproduce the 20 kHz sine
wave accurately.

Just over 2 samples are all that is needed to define a unique sine wave,
both amplitude and phase (timing). That's one of those things that you learn
from trigonometry, if perchance you study and remember it.

All that the Nyquist limit guarantees
is that you can detect a 20 kHz wave (ie. yes, a 20 kHz
wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

Yes 40.000 KHz won't work, but 40.0000000000000001 KHz will. All you need
is just over 2 samples to define that unique sine wvae.

This seems to argue for a sampling rate of 4 or 5 times
the Nyquist minimum limit.

Not at all. Furthermore, this all works out in the lab. It's not an esoteric
theory, it is how things work.

Perhaps this is why DVD sampling is at 192 kHz?

There is no sonic justification for such high sample rates as 192 KHz. If
you try to go the opposite way, you'll find that sampling rates as low as 32
KHz are "music friendly".

[Arny Krueger]

"Soundhaspriority" wrote in message

wrote in message
ups.com...
On May 2, 12:23 pm, "Soundhaspriority"
wrote:
wrote in message

oups.com...
[snip]



Surely you'd need about four or five samples per
half-cycle to even hope to reproduce the 20 kHz sine
wave accurately. All that the Nyquist limit guarantees
is that you can detect a 20 kHz wave (ie. yes, a 20
kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5
times the Nyquist minimum limit. Perhaps this is why
DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be
interested in the flaws in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The
wave is reconstructed by an algorithm or by an analog
filter. As the Nyquist limit
is approached, the problem acquires infinite
complexity. What actually happens is that the
reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as
phase shift, which is one of the reasons higher
sampling rates are preferred.

In a word, bullsh*t.

It does NOT manifest itself as phase shift. Typical
phase shift errorsof a the vast majority of 44.1 kHz
sampling systems are less than a dozen or so degeres right up to cutoff.

The oft-disproven arrogant intellectual failure spews:

You are WRONG.

No, Dick Pierce is right.

Here is a real-world example that supports his claim - actually makes him
look maybe a bit conservative.

http://www.pcavtech.com/soundcards/l...644-xfus10.gif

44 KHz sampling, and about 5 degrees off at 20 KHz.

[Stéphane Guillard]

Hi,

Although at first thoughts you sound right, what is missing in your vision
is the low pass filter which is used during analog reconstruction, which if
implemented right, forces your close-to-limit samples into a sinewave. Think
about it in terms of frequency-windowed Fourier Transform series, your high
freq samples represent the energy for that high frequency... sinewave. The
low pass filter will reject anything that would let it become a square or
whatever.

Regards,
--
Stéphane

a écrit dans le message de news:
...
For some years now the Nyquist Sampling Theorem has been bugging me
and I've decided to come public because none of what I've read
adresses my concern - not directly anyway.

As you all know, the Nyquist theorem states that "Exact
reconstruction of a continuous-time baseband signal from its samples
is possible if the signal is bandlimited and the sampling frequency is
greater than twice the signal bandwidth".

Now if I sample a 1 Hz waveform with a sampling rate of just over 40
kHz then I'd expect to see just over 40 thousand samples for that
single-cycle wave - 20 thousand samples for the positive half and
another 20 thousand for the negative half.

Now go right up to 20 kHz. I get ONE sample in the positive half and
ONE sample in the negative half! That's not too impressive is it? Just
how are you going to reconstruct a 20 kHz wave accurately with just
one sample per half-cycle. That sample could have landed anywhere on
the sine-curve - so how do you know what the maximum amplitude of that
20 kHz wave is?

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

[Randy Yates]

(Don Pearce) writes:
[...]
What do you mean by "if" the A/D oversamples (and I presume you
include the D/A in that).

Which part of the word "if" don't you understand?

I can't think of a single example of one that doesn't. As far as I
am concerned it is a vital part of the process.

You are probably correct in the audio world. I was not constraining
the discussion to audio A/Ds.
--
% Randy Yates % "With time with what you've learned,
%% Fuquay-Varina, NC % they'll kiss the ground you walk
%%% 919-577-9882 % upon."
%%%% % '21st Century Man', *Time*, ELO
http://home.earthlink.net/~yatescr

[Don Pearce]

On Thu, 03 May 2007 08:53:31 -0400, Randy Yates
wrote:

(Don Pearce) writes:
[...]
What do you mean by "if" the A/D oversamples (and I presume you
include the D/A in that).

Which part of the word "if" don't you understand?

I understand "if" perfectly. My confusion is in that you would think
of using the word - but you have explained below. I think that for the
purposes of this group we should stick to audio. Things are confused
enough already without straying too far away from sound reproduction.

I can't think of a single example of one that doesn't. As far as I
am concerned it is a vital part of the process.

You are probably correct in the audio world. I was not constraining
the discussion to audio A/Ds.


d

--
Pearce Consulting
http://www.pearce.uk.com

[Randy Yates]

(Don Pearce) writes:

On Thu, 03 May 2007 08:53:31 -0400, Randy Yates
wrote:

(Don Pearce) writes:
[...]
What do you mean by "if" the A/D oversamples (and I presume you
include the D/A in that).

Which part of the word "if" don't you understand?

I understand "if" perfectly. My confusion is in that you would think
of using the word - but you have explained below. I think that for the
purposes of this group we should stick to audio. Things are confused
enough already without straying too far away from sound reproduction.

For most posts in this group I would agree. However, if we go back
through the history of this thread to the original question by Eddy,
the scope is necessarily bigger than audio.
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

[Don Pearce]

On Thu, 03 May 2007 09:21:11 -0400, Randy Yates
wrote:

(Don Pearce) writes:

On Thu, 03 May 2007 08:53:31 -0400, Randy Yates
wrote:

(Don Pearce) writes:
[...]
What do you mean by "if" the A/D oversamples (and I presume you
include the D/A in that).

Which part of the word "if" don't you understand?

I understand "if" perfectly. My confusion is in that you would think
of using the word - but you have explained below. I think that for the
purposes of this group we should stick to audio. Things are confused
enough already without straying too far away from sound reproduction.

For most posts in this group I would agree. However, if we go back
through the history of this thread to the original question by Eddy,
the scope is necessarily bigger than audio.

Sure, but his question was about Nyquist rate and the reconstruction
of a sine wave. That was all kind of dealt with, and the thread has
moved on. The reconstruction filter phase response sub-thread is
decidedly audio-related.

d

--
Pearce Consulting
http://www.pearce.uk.com

[Randy Yates]

(Don Pearce) writes:

Sure, but his question was about Nyquist rate and the reconstruction
of a sine wave. That was all kind of dealt with, and the thread has
moved on. The reconstruction filter phase response sub-thread is
decidedly audio-related.

It is apparent you think so.
--
% Randy Yates % "Remember the good old 1980's, when
%% Fuquay-Varina, NC % things were so uncomplicated?"
%%% 919-577-9882 % 'Ticket To The Moon'
%%%% % *Time*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

[Don Pearce]

On Thu, 03 May 2007 09:40:04 -0400, Randy Yates
wrote:

(Don Pearce) writes:

Sure, but his question was about Nyquist rate and the reconstruction
of a sine wave. That was all kind of dealt with, and the thread has
moved on. The reconstruction filter phase response sub-thread is
decidedly audio-related.

It is apparent you think so.

Whatever. You seem to be angling for a row about this, but frankly I'm
not interested. It just isn't important.

d

--
Pearce Consulting
http://www.pearce.uk.com

[Walt]

wrote:

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?


DVD's have a bitrate of 192k bits per second. That's not the same thing
as the sampling rate.

Many good responses above regarding the math behind the Nyquist theorem.
Not much for me to add there.

//Walt

[Mogens V.]

Randy Yates wrote:
"Soundhaspriority" writes:


wrote in message
roups.com...

On May 2, 12:23 pm, "Soundhaspriority" wrote:

wrote in message

legroups.com...
[snip]




Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist
limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

In a word, bullsh*t.

It does NOT manifest itself as phase shift. Typical phase shift
errorsof a the vast majority of 44.1 kHz sampling systems
are less than a dozen or so degeres right up to cutoff.


You are WRONG.


I think it depends on the architecture used in the A/D.

If the A/D runs at the final sample rate (e.g., 44.1 kHz), then the
analog filter must be sharp, and there would be significant phase
distortion near Fs/2.

Says who? It very much depends on the chosen type of filter.
For elliptic filters (Chebychef, Legendre..) yes; for Bessel types no.
Yes, Bessel filters require more orders, but remains at a constant rate,
in contrast to elliptic filters, which tend to flaten out again, albeit
somewhat down the amplitude. Pls excuse me if I remember incorrectly.


--
Kind regards,
Mogens V.

[Randy Yates]

"Mogens V." writes:

Randy Yates wrote:
"Soundhaspriority" writes:

wrote in message
ups.com...

On May 2, 12:23 pm, "Soundhaspriority" wrote:

wrote in message

glegroups.com...
[snip]




Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the
Nyquist limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

In a word, bullsh*t.

It does NOT manifest itself as phase shift. Typical phase shift
errorsof a the vast majority of 44.1 kHz sampling systems
are less than a dozen or so degeres right up to cutoff.


You are WRONG.
I think it depends on the architecture used in the A/D. If the A/D
runs at the final sample rate (e.g., 44.1 kHz), then the
analog filter must be sharp, and there would be significant phase
distortion near Fs/2.

Says who? It very much depends on the chosen type of filter.
For elliptic filters (Chebychef, Legendre..) yes; for Bessel types no.
Yes, Bessel filters require more orders, but remains at a constant
rate, in contrast to elliptic filters, which tend to flaten out again,
albeit somewhat down the amplitude. Pls excuse me if I remember
incorrectly.

Point taken. See, e.g., [proakis].

--Randy

@BOOK{proakis,
title = "{Digital Signal Processing: Principles, Algorithms, and Applications}",
author = "John~G.~Proakis and Dimitris~G.~Manolakis",
publisher = "Prentice Hall",
edition = "third",
year = "1996"}

--
% Randy Yates % "Midnight, on the water...
%% Fuquay-Varina, NC % I saw... the ocean's daughter."
%%% 919-577-9882 % 'Can't Get It Out Of My Head'
%%%% % *El Dorado*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

[Geoff]

Randy Yates wrote:
I think it depends on the architecture used in the A/D.

If the A/D runs at the final sample rate (e.g., 44.1 kHz), then the
analog filter must be sharp, and there would be significant phase
distortion near Fs/2.

Suh A/Ds (surely) were superceded by the end of the 80s ?!!!

If the A/D oversamples, then the filter requirement is relaxed and
the phase shift may be relatively benign at Fs/2.

And higher for higher ...


I have to admit, as much as I respect Dick, that I must agree with
you, Bob, in this particular context and discussion.

But not in the ciontext of current and recent practice.

geoff

[Randy Yates]

"Geoff" writes:

Randy Yates wrote:
I think it depends on the architecture used in the A/D.

If the A/D runs at the final sample rate (e.g., 44.1 kHz), then the
analog filter must be sharp, and there would be significant phase
distortion near Fs/2.

Suh A/Ds (surely) were superceded by the end of the 80s ?!!!

Let's not get too tunnel-visioned here, folks. There are other
applications of digital other than to audio. So, no, such A/Ds were
NOT superceded by the end of the 80s.

I have to admit, as much as I respect Dick, that I must agree with
you, Bob, in this particular context and discussion.

But not in the ciontext of current and recent practice.

As I stated, yes, even in current practice. But I'm not constraining
my consideration to audio applications.
--
% Randy Yates % "Ticket to the moon, flight leaves here today
%% Fuquay-Varina, NC % from Satellite 2"
%%% 919-577-9882 % 'Ticket To The Moon'
%%%% % *Time*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

[Codifus]

On May 3, 7:23 am, "Arny Krueger" wrote:

There is no sonic justification for such high sample rates as 192 KHz. If
you try to go the opposite way, you'll find that sampling rates as low as 32
KHz are "music friendly".

I think there is a sonic justification, and you actually pointed me in
the right direction. Some years ago I got into soundcards and found
your site, PCAVTECH. Then I starting browsing the newgroups and
learned, from you and others, that a 16 bit soundcard cannot fully
reproduce all 16 bits of dynamic range. Even a 24 bit soundcard can't
produce 16 bits of dynamic range perfectly, and it's supposed to
produce 144 db of S/N or dynamics.

My point is that electronics are not perfect and do not act ideally. A
44.1Khz /16 signal being reproduced by imperfect electronics doesn't
reproduce the audio signal as perfectly as it should, but is still way
better than any analog. So it goes to follow that a 192/24 system
based on the same imperfect electronics, will have a much easier time
reproducing 16 bits of dynamic range and a frequency response to 20
Khz and somehwat beyond better than a 44.1/16 system will.


CD

[Mr.T]

"Walt" wrote in message
...
wrote:

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?


DVD's have a bitrate of 192k bits per second. That's not the same thing
as the sampling rate.

He probably meant DVD-A which can have a sampling rate of 192kHz, if for no
other reason than it's possible.

BTW video DVD is usually higher than 192kbs, but of course you are talking
compressed MP3/AAC in that case, not HiFi anyway. Some have an uncompressed
PCM alternative, but usually 48kHz sample rate.

MrT.

[Mr.T]

"codifus" wrote in message
ups.com...
I think there is a sonic justification, and you actually pointed me in
the right direction. Some years ago I got into soundcards and found
your site, PCAVTECH. Then I starting browsing the newgroups and
learned, from you and others, that a 16 bit soundcard cannot fully
reproduce all 16 bits of dynamic range. Even a 24 bit soundcard can't
produce 16 bits of dynamic range perfectly,

Sure they can, when used at 24 bits. Arny's tests prove just that!
And some come amazingly close to perfection even when used at the 16/44
rate.
Check out the Lynx2 tests for proof.
If only our auditory system was that good! :-)

My point is that electronics are not perfect and do not act ideally. A
44.1Khz /16 signal being reproduced by imperfect electronics doesn't
reproduce the audio signal as perfectly as it should, but is still way
better than any analog. So it goes to follow that a 192/24 system
based on the same imperfect electronics, will have a much easier time
reproducing 16 bits of dynamic range and a frequency response to 20
Khz and somehwat beyond better than a 44.1/16 system will.

Of course, simply select how much overkill you are prepared to pay for, your
ears won't tell the difference though.

MrT.

[Mr.T]

"Don Pearce" wrote in message
...
What do you mean by "if" the A/D oversamples (and I presume you
include the D/A in that). I can't think of a single example of one
that doesn't. As far as I am concerned it is a vital part of the
process.

"IF" seems quite appropriate. Not all audio A/D-D/A used oversampling in the
past, and he never limited his statement to what is currently being made, so
why the need for argument?

MrT.

[Karl Uppiano]

"Soundhaspriority" wrote in message
...

wrote in message
oups.com...
[snip]

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which is
one of the reasons higher sampling rates are preferred.

A Finite Impulse Response digital filter is phase linear, and it can be as
"brick wall" as you want to make it. It just takes more registers (and more
time to compute).

[Karl Uppiano]

"Soundhaspriority" wrote in message
...

"Steven Sullivan" wrote in message
...
Soundhaspriority wrote:

wrote in message
oups.com...
[snip]

Surely you'd need about four or five samples per half-cycle to even
hope to reproduce the 20 kHz sine wave accurately. All that the
Nyquist limit guarantees is that you can detect a 20 kHz wave (ie.
yes, a 20 kHz wave exists) but at a sampling rate of 40 kHz you
certainly can't reproduce the wave accurately.

This seems to argue for a sampling rate of 4 or 5 times the Nyquist
minimum limit. Perhaps this is why DVD sampling is at 192 kHz?

Don't shoot me down in flames please. I'd be interested in the flaws
in my reasoning that all :-)

Cheers

Eddy

Eddy,
Your concern is practically speaking, correct. The wave is
reconstructed by an algorithm or by an analog filter. As the Nyquist
limit
is approached, the problem acquires infinite complexity. What actually
happens is that the reconstruction gradually deteriorates as the Nyquist
"brick wall" is encountered. The error manifests as phase shift, which
is
one of the reasons higher sampling rates are preferred.

You will probably find this ignites a "flame war", but stick to your
guns. You're right.

As I understand it, this is not a problem if oversampling is used. And
if it isn't (rare
nowadays), it's not a problem *if* the player's filters are
well-implemented, in which case
the phase shift should be practically inaudible. The technical
difficulty/cost-effectiveness
of implementing such filtering is the reason why oversampling has been
the norm for years now
in CD players.

It is a problem at some point near the Nyquist frequency. Remember that
the filters are implemented by analytic functions. An analytic function
doesn't behave nice near a point and then go singular at that point. The
closer to the Nyquist frequency, the more the construction falls apart.
Since music is not composed of a continuous sine wave, there is the very
real problem of how to fit a finite number of points with the appropriate
continuous function. It falls apart as phase shift, in some neighborhood
of the Nyquist frequency, no matter how thorough one has been at designing
the filter.

It doesn't matter if the music is composed of a continuous sine wave. If the
22.05KHz filter can reconstruct 20KHz perfectly, it can reconstruct anything
and everything below that, perfectly as well, whether it is a mixture of
frequencies or not, as long as none of them exceeds 22.05 KHz.

[Karl Uppiano]

We've had FM stereo for 40 years and nobody said a word about brick wall
filters or the Nyquist sampling theorem, but as soon as the compact disc
came out, everyone was suspicious of sampled technology.

FM stereo uses a 38 KHz suppressed subcarrier, with a 19 KHz pilot tone,
phase locked at the Nyquist frequency (effectively a zero-beat with the
suppressed carrier). The analog filters of the 60s and 70s were neither
phase linear nor particularly brick wall (they started rolling off at around
15 KHz, and they were not down all that far at 19 KHz).

Now, I realize that most audiophiles will sneer in derision at FM as an
audio source, but FM done right (which happens all too rarely) actually
sounds very good. Most of the sound quality goes out the window at the point
where it hits the AGC/multiband compressor/multiband
limiter/clipper/composite clipper (all intended to give the station the
phattest sound on the dial -- whooptee-doo). The main problem is with the
standards and practices, not the technology.

Today's stereo generators (without all of the audio processing) could
probably deliver nearly 18 KHz of phase-linear audio with near zero
aliasing. I doubt the receivers have improved much in the last 30 years,
though.

[Don Pearce]

On Fri, 04 May 2007 06:59:34 GMT, "Karl Uppiano"
wrote:

We've had FM stereo for 40 years and nobody said a word about brick wall
filters or the Nyquist sampling theorem, but as soon as the compact disc
came out, everyone was suspicious of sampled technology.

FM stereo uses a 38 KHz suppressed subcarrier, with a 19 KHz pilot tone,
phase locked at the Nyquist frequency (effectively a zero-beat with the
suppressed carrier). The analog filters of the 60s and 70s were neither
phase linear nor particularly brick wall (they started rolling off at around
15 KHz, and they were not down all that far at 19 KHz).

Now, I realize that most audiophiles will sneer in derision at FM as an
audio source, but FM done right (which happens all too rarely) actually
sounds very good. Most of the sound quality goes out the window at the point
where it hits the AGC/multiband compressor/multiband
limiter/clipper/composite clipper (all intended to give the station the
phattest sound on the dial -- whooptee-doo). The main problem is with the
standards and practices, not the technology.

Today's stereo generators (without all of the audio processing) could
probably deliver nearly 18 KHz of phase-linear audio with near zero
aliasing. I doubt the receivers have improved much in the last 30 years,
though.


Just one problem here. FM Stereo isn't sampled, so it doesn't have a
Nyquist frequency. I guess that could be why nobody was talking about
Nyquist sampling theorem?

d

--
Pearce Consulting
http://www.pearce.uk.com

[Codifus]

On May 3, 11:51 pm, "Mr.T" MrT@home wrote:
"codifus" wrote in message

ups.com...

I think there is a sonic justification, and you actually pointed me in
the right direction. Some years ago I got into soundcards and found
your site, PCAVTECH. Then I starting browsing the newgroups and
learned, from you and others, that a 16 bit soundcard cannot fully
reproduce all 16 bits of dynamic range. Even a 24 bit soundcard can't
produce 16 bits of dynamic range perfectly,

Sure they can, when used at 24 bits. Arny's tests prove just that!
And some come amazingly close to perfection even when used at the 16/44
rate.
Check out the Lynx2 tests for proof.
Yes, I've heard of theLynx2, and also the DAC1 Not a soundcard but a
very well regarded D/A converter.

If only our auditory system was that good! :-)

That's just my point. SOME soundcards do very well. Can you say that
any soundcard that isn't a Lynx is of inferior electronic design?
Perhaps they are. And maybe 10 years from now when any Lynx patent
might run out all the soundacrd manufacturers from Creative to
EchoAudio may run out and copy the Lynx design and everything would be
perfect.


My point is that electronics are not perfect and do not act ideally. A
44.1Khz /16 signal being reproduced by imperfect electronics doesn't
reproduce the audio signal as perfectly as it should, but is still way
better than any analog. So it goes to follow that a 192/24 system
based on the same imperfect electronics, will have a much easier time
reproducing 16 bits of dynamic range and a frequency response to 20
Khz and somehwat beyond better than a 44.1/16 system will.

Of course, simply select how much overkill you are prepared to pay for, your
ears won't tell the difference though.

Maybe, maybe not. Fact is, CDs were "perfect sound forever" and we've
realized just how flawed it was at the beginning. It took about 20
years for CD to mature to the very good state that it's in now.

Because it all depends, I wouldn't count out the higher rez formats as
un-necessary or overkill.

MrT.

CD

[Serge Auckland]

codifus wrote:
On May 3, 11:51 pm, "Mr.T" MrT@home wrote:
"codifus" wrote in message

ups.com...

I think there is a sonic justification, and you actually pointed me in
the right direction. Some years ago I got into soundcards and found
your site, PCAVTECH. Then I starting browsing the newgroups and
learned, from you and others, that a 16 bit soundcard cannot fully
reproduce all 16 bits of dynamic range. Even a 24 bit soundcard can't
produce 16 bits of dynamic range perfectly,
Sure they can, when used at 24 bits. Arny's tests prove just that!
And some come amazingly close to perfection even when used at the 16/44
rate.
Check out the Lynx2 tests for proof.
Yes, I've heard of theLynx2, and also the DAC1 Not a soundcard but a
very well regarded D/A converter.

If only our auditory system was that good! :-)

That's just my point. SOME soundcards do very well. Can you say that
any soundcard that isn't a Lynx is of inferior electronic design?
Perhaps they are. And maybe 10 years from now when any Lynx patent
might run out all the soundacrd manufacturers from Creative to
EchoAudio may run out and copy the Lynx design and everything would be
perfect.

My point is that electronics are not perfect and do not act ideally. A
44.1Khz /16 signal being reproduced by imperfect electronics doesn't
reproduce the audio signal as perfectly as it should, but is still way
better than any analog. So it goes to follow that a 192/24 system
based on the same imperfect electronics, will have a much easier time
reproducing 16 bits of dynamic range and a frequency response to 20
Khz and somehwat beyond better than a 44.1/16 system will.
Of course, simply select how much overkill you are prepared to pay for, your
ears won't tell the difference though.

Maybe, maybe not. Fact is, CDs were "perfect sound forever" and we've
realized just how flawed it was at the beginning. It took about 20
years for CD to mature to the very good state that it's in now.

Because it all depends, I wouldn't count out the higher rez formats as
un-necessary or overkill.
MrT.

CD


And yet.... CDs now are generally of poorer audio quality than 10-15
years ago due to excessive processing at the mastering stage reducing
dynamic range and introducing deliberate clipping to increase loudness.

Some of the early CDs were poor due to ignorance of the new medium, when
masters equalised and compressed for Vinyl were used to master CDs. It
was soon realised that for CD new masters had to be produced, but this
lesson was learned quite early on, say, buy around 1985-6. This means
that we had some 10 years in which CD was as close to "pure perfect
sound" as was possible at the time, and has rarely been bettered since.

The new higher resolution formats are, at least for me, overkill for
domestic sound reproduction, but nevertheless, it's good to have them if
only for archival purposes.

S.
--
http://audiopages.googlepages.com