So, here's my question. If I digitize a 15 kHz signal, using a 44.1 kHz
sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz singal with
varying amplitude? How accurate is that signal, is there no lag in the
reconstructed signal? I mean, if the amplitude of the original changes, is
the reconstructed signal as true at 15 kHz as at 4 kHz?

This to me is a far more important concern than whether I can hear 20+kHz
signals.

Thanks for your intelligent and well thought out replies. The rest of you
can suck my electric outlet.

Erik

"Erik Squires" wrote in message
ervers.com...
So, here's my question. If I digitize a 15 kHz signal, using a 44.1 kHz
sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz singal
with
varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure 15 kHz.
There has to be another component imposed on the
15 kHz that "varies the amplitude".

ScottW

"Erik Squires" wrote in message
ervers.com

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

OK

Are the normal digital filters good enough to reproduce a 15 kHz
signal with varying amplitude?

Yes.

How accurate is that signal

Incredibly accurate, by analog standards.

is there no lag in the reconstructed signal?

Compared to a concurrent signal at 1 KHz, the lag can be less than there is
in a good analog power amplifier or preamp.

I mean, if the amplitude of the
original changes, is the reconstructed signal as true at 15 kHz as at
4 kHz?

Yes. 4 KHz and 15 KHz sine waves can be reconstructed with equal accuracy.

This to me is a far more important concern than whether I can hear
20+kHz signals.

Worry not.

"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that "varies the
amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient.

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Arny is an again proving he knows very little about
everything. In fact he has a degree in it.

ScottW

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that "varies the
amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique
frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient.

Wrong.
Arny is simplistically parroting the Nyquist Theorem, which states that any
signal can be reconstructed with a sampling rate twice the maximum frequency
present in the signal.
This, however, is a theoretical result. It is impossible to implement in
practice, because the analog reconstruction filter required would have to
cut off instantaneously at 15kHz. Since it can't, the result would be a 15
kHz signal with higher harmonics
To understand what happens if the reconstruction filter is not present, 2X
sampling would provide a simple 15 khz square wave. To the extent that the
square wave is not brick wall, some of the harmonic structure of the
corresponding square wave will be present.

In theory, using noncausal filtering, it's possible to make the brick wall
filter. In practice, it can't be done.
One of the original innovations in CD DACs was the oversampling DAC. In this
approach, the signal is interpolated using a digital filter chip. It is a
form of upsampling. The upsampled signal is easier to filter.
Unfortunately, the implementation of digital interpolation algorithms
remains to this day an incompletely solved problem.

Recently, Arny brought forth a recent AES paper that purported to show that
signals above 20 kHz make no difference in the perceived quality of the
reproduction. There is a considerable body of evidence that the ear can't
hear above 20 kHz, yet many listeners report improved fidelity with higher
sampling rates and greater bit depth. The most probable explanation of this
lies with the reduced phase of enhanced/upsampled/high bit rate systems
shift at frequencies approaching 20 kHz.

On Sat, 22 Nov 2003 21:07:24 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that "varies the
amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient.


Arny,
I am probably looking at this the wrong way, using an
oversimplified model, but I can't see how a sine wave can be
completely defined by three points.
I'm picturing a sine wave plotted with time along the x-axis,
and amplitude along the y-axis. If I tell you that the amplitudes at
zero seconds, 1 second, and 2 seconds are all zero, I've given you
three different points along the wave. From this, the period can be
measured and the frequency derived from that, but I don't see how I've
given you enough information to calculate the amplitude.
Let me know what I'm missing. Do the three points have to
have non-zero amplitude for them to be used to define the waveform?

Thanks,
Scott Gardner

"ScottW" wrote in message
news:VPVvb.4621$ML6.516@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Arny is an again proving he knows very little about
everything. In fact he has a degree in it.

You're either incredibly stupid Scott, or you're lying.

"Robert Morein" wrote in message

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
signal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that
"varies the amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique
frequency, phase and amplitude. In fact, just slightly more than two
samples is sufficient.

Wrong.

Right.

Arny is simplistically parroting the Nyquist Theorem, which states
that any signal can be reconstructed with a sampling rate twice the
maximum frequency present in the signal.

Wrong. The sampling rate has to be slightly higher than twice.

This, however, is a theoretical result. It is impossible to implement
in practice, because the analog reconstruction filter required would
have to cut off instantaneously at 15kHz.

Since the sample rate has been stated to be 44.1 KHz, the reconstruction
filter needs to cut off slightly below 22.05 KHz, not 15 KHz. In the case of
a 15 KHz signal, this gives a 7.05 KHz range in which the filter needs to
cut off.

Since it can't, the result
would be a 15 kHz signal with higher harmonics

Wrong.

To understand what happens if the reconstruction filter is not
present, 2X sampling would provide a simple 15 kHz square wave. To
the extent that the square wave is not brick wall, some of the
harmonic structure of the corresponding square wave will be present.

Wrong, the sample rate was stated to be 44.1 KHz.

In theory, using noncausal filtering, it's possible to make the brick
wall filter. In practice, it can't be done.

As I've shown, there is a 7.05 KHz range in which the reconstruction filter
must cut off, in order to reproduce a 15 KHz signal with 44.1 KHz sampling.

One of the original innovations in CD DACs was the oversampling DAC.
In this approach, the signal is interpolated using a digital filter
chip. It is a form of upsampling. The upsampled signal is easier to
filter. Unfortunately, the implementation of digital interpolation
algorithms remains to this day an incompletely solved problem.

Wrong. The problem has been solved quite nicely thank you, and for at least
a decade.

Recently, Arny brought forth a recent AES paper that purported to
show that signals above 20 kHz make no difference in the perceived
quality of the reproduction. There is a considerable body of evidence
that the ear can't hear above 20 kHz, yet many listeners report
improved fidelity with higher sampling rates and greater bit depth.

That's because these listeners don't use appropriate experimental controls
when they do their listening tests.

The most probable explanation of this lies with the reduced phase of
enhanced/upsampled/high bit rate systems shift at frequencies
approaching 20 kHz.

The most probably explanation is that these listeners don't use appropriate
experimental controls when they do their listening tests, and therefore they
produce bogus results.

"Scott Gardner" wrote in message

On Sat, 22 Nov 2003 21:07:24 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that
"varies the amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique
frequency, phase and amplitude. In fact, just slightly more than two
samples is sufficient.


Arny,
I am probably looking at this the wrong way, using an
oversimplified model, but I can't see how a sine wave can be
completely defined by three points.

It's a theorem that has never been disproved that says that it takes
slightly more than 2 points to adequately define a unique sine wave.

I'm picturing a sine wave plotted with time along the x-axis,
and amplitude along the y-axis. If I tell you that the amplitudes at
zero seconds, 1 second, and 2 seconds are all zero, I've given you
three different points along the wave.

Right, but the frequency of that wave has to be outside the range for which
the theorem applies.

From this, the period can be
measured and the frequency derived from that, but I don't see how I've
given you enough information to calculate the amplitude.
Let me know what I'm missing.

You are missing the fact that the frequency of a signal with three points
that are zero is too high for the Nyquist theorem to apply. In fact, the
frequency of the signal has to be exactly half the sample rate.

Do the three points have to
have non-zero amplitude for them to be used to define the waveform?

At least one of the points has to be non-zero, and this will be true if the
frequency of the signal is even just slightly below half the sample rate. At
exactly half the sample rate, the signal can have any amplitude and have
three zero samples. It's a well-known boundary condition.

On Sun, 23 Nov 2003 04:04:38 -0500, "Arny Krueger"
wrote:

"Scott Gardner" wrote in message

On Sat, 22 Nov 2003 21:07:24 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that
"varies the amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique
frequency, phase and amplitude. In fact, just slightly more than two
samples is sufficient.


Arny,
I am probably looking at this the wrong way, using an
oversimplified model, but I can't see how a sine wave can be
completely defined by three points.

It's a theorem that has never been disproved that says that it takes
slightly more than 2 points to adequately define a unique sine wave.

I'm picturing a sine wave plotted with time along the x-axis,
and amplitude along the y-axis. If I tell you that the amplitudes at
zero seconds, 1 second, and 2 seconds are all zero, I've given you
three different points along the wave.

Right, but the frequency of that wave has to be outside the range for which
the theorem applies.

From this, the period can be
measured and the frequency derived from that, but I don't see how I've
given you enough information to calculate the amplitude.
Let me know what I'm missing.

You are missing the fact that the frequency of a signal with three points
that are zero is too high for the Nyquist theorem to apply. In fact, the
frequency of the signal has to be exactly half the sample rate.

Do the three points have to
have non-zero amplitude for them to be used to define the waveform?

At least one of the points has to be non-zero, and this will be true if the
frequency of the signal is even just slightly below half the sample rate. At
exactly half the sample rate, the signal can have any amplitude and have
three zero samples. It's a well-known boundary condition.


Okay, that makes sense to me now. Since the three points I
chose were at zero, one and two seconds, my sampling rate was
therefore 1 Hz. Since the amplitudes at all three points were zero,
they therefore represented the start, crossover, and end of a waveform
with a period of two seconds, or a frequency of 1/2 Hz. Since the
frequency of my waveform (1/2 Hz) was greater than or equal to half of
my sampling rate (1 Hz), there wasn't enough information there to
determine the waveform characteristics.

Thanks for the clarification. I still remembered how to do
polynomial curve fitting, based on the number of local minima and
maxima in the plot of the polynomial, but if I ever learned
trigonometric curve fitting, I had obviously forgotten it.

Scott Gardner

"Scott Gardner" wrote in message

On Sun, 23 Nov 2003 04:04:38 -0500, "Arny Krueger"
wrote:

"Scott Gardner" wrote in message

On Sat, 22 Nov 2003 21:07:24 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that
"varies the amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique
frequency, phase and amplitude. In fact, just slightly more than
two samples is sufficient.


Arny,
I am probably looking at this the wrong way, using an
oversimplified model, but I can't see how a sine wave can be
completely defined by three points.

It's a theorem that has never been disproved that says that it takes
slightly more than 2 points to adequately define a unique sine wave.

I'm picturing a sine wave plotted with time along the x-axis,
and amplitude along the y-axis. If I tell you that the amplitudes
at zero seconds, 1 second, and 2 seconds are all zero, I've given
you three different points along the wave.

Right, but the frequency of that wave has to be outside the range
for which the theorem applies.

From this, the period can be
measured and the frequency derived from that, but I don't see how
I've given you enough information to calculate the amplitude.
Let me know what I'm missing.

You are missing the fact that the frequency of a signal with three
points that are zero is too high for the Nyquist theorem to apply.
In fact, the frequency of the signal has to be exactly half the
sample rate.

Do the three points have to
have non-zero amplitude for them to be used to define the waveform?

At least one of the points has to be non-zero, and this will be true
if the frequency of the signal is even just slightly below half the
sample rate. At exactly half the sample rate, the signal can have
any amplitude and have three zero samples. It's a well-known
boundary condition.

Okay, that makes sense to me now. Since the three points I
chose were at zero, one and two seconds, my sampling rate was
therefore 1 Hz. Since the amplitudes at all three points were zero,
they therefore represented the start, crossover, and end of a waveform
with a period of two seconds, or a frequency of 1/2 Hz. Since the
frequency of my waveform (1/2 Hz) was greater than or equal to half of
my sampling rate (1 Hz), there wasn't enough information there to
determine the waveform characteristics.

Bingo!

Thanks for the clarification. I still remembered how to do
polynomial curve fitting, based on the number of local minima and
maxima in the plot of the polynomial, but if I ever learned
trigonometric curve fitting, I had obviously forgotten it.

Thanks for correctly perceiving my explanation.

There are at least three forms of curve-fitting that I've seen used pretty
frequently:

(1) Polynomial
(2) Exponential
(3) Trigonometric

I seem to recall that all that is required is that the curve-fitting
methodology be based on orthogonal functions, and that's only a requirement
if you want a general, unique solution.

On Sun, 23 Nov 2003 04:11:24 GMT, (Scott Gardner)
wrote:

On Sat, 22 Nov 2003 21:07:24 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that "varies the
amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient.


Arny,
I am probably looking at this the wrong way, using an
oversimplified model, but I can't see how a sine wave can be
completely defined by three points.

A pure sine wave has infinite length which is more than three points
in total. This makes a difference.


I'm picturing a sine wave plotted with time along the x-axis,
and amplitude along the y-axis. If I tell you that the amplitudes at
zero seconds, 1 second, and 2 seconds are all zero, I've given you
three different points along the wave. From this, the period can be
measured and the frequency derived from that, but I don't see how I've
given you enough information to calculate the amplitude.
Let me know what I'm missing. Do the three points have to
have non-zero amplitude for them to be used to define the waveform?

Thanks,
Scott Gardner

"Arny Krueger" wrote in message
...
"Robert Morein" wrote in message

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...



Since the sample rate has been stated to be 44.1 KHz, the reconstruction
filter needs to cut off slightly below 22.05 KHz, not 15 KHz. In the case
of
a 15 KHz signal, this gives a 7.05 KHz range in which the filter needs to
cut off.

Unfortunately, I misread the question.
Your mathematical analysis is basically correct.
However, your statement that the reconstruction filter problem has been
solved is not correct, and probably accounts for the small variations in
perceived quality among DACs.

A digital reconstruction filter cannot be perfect unless it has infinite run
length and is noncausal. While digital filters are typically noncausal, they
have limited run length.

Likewise for the analog filter. However, the run length of an analog filter
is even more severly restricted.

The reconstruction filter remains the weak link in DAC design.

Robert:

Right, I think the debate over 40 kHz signals and whether or not they have
any effect on us at all is cool, but not what I wanted to ask.

I'm more concerned with how good 3 samples is at 15 kHz, which I can hear,
albeit weaker every year.

So, 3 points in time, separated by 1/44,100 of a second, with 15 bits of
resolution (plus the polarity bit). Can this really define any sine wave
accurately? What about a decaying sine wave, one who's amplitude is
decreasing linearly or logarithmically with time? Can a mere 3 points
really stay true to this, even without getting into discusisons of linearity
of a DAC at -90 db.

This is my real interest in high frequency recordings. I don't intend to go
out and buy a super tweeter.

Thanks!


Erik

"Robert Morein" wrote in message
...

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

There has to be another component imposed on the 15 kHz that "varies
the
amplitude".

Wrong.

Three samples is sufficient to define a sine wave that has unique
frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient.

Wrong.
Arny is simplistically parroting the Nyquist Theorem, which states that
any
signal can be reconstructed with a sampling rate twice the maximum
frequency
present in the signal.
This, however, is a theoretical result. It is impossible to implement in
practice, because the analog reconstruction filter required would have to
cut off instantaneously at 15kHz. Since it can't, the result would be a 15
kHz signal with higher harmonics
To understand what happens if the reconstruction filter is not present, 2X
sampling would provide a simple 15 khz square wave. To the extent that the
square wave is not brick wall, some of the harmonic structure of the
corresponding square wave will be present.

In theory, using noncausal filtering, it's possible to make the brick wall
filter. In practice, it can't be done.
One of the original innovations in CD DACs was the oversampling DAC. In
this
approach, the signal is interpolated using a digital filter chip. It is a
form of upsampling. The upsampled signal is easier to filter.
Unfortunately, the implementation of digital interpolation algorithms
remains to this day an incompletely solved problem.

Recently, Arny brought forth a recent AES paper that purported to show
that
signals above 20 kHz make no difference in the perceived quality of the
reproduction. There is a considerable body of evidence that the ear can't
hear above 20 kHz, yet many listeners report improved fidelity with higher
sampling rates and greater bit depth. The most probable explanation of
this
lies with the reduced phase of enhanced/upsampled/high bit rate systems
shift at frequencies approaching 20 kHz.

"Erik Squires" wrote in message
rvers.com
Robert:

Right, I think the debate over 40 kHz signals and whether or not they
have any effect on us at all is cool, but not what I wanted to ask.

I'm more concerned with how good 3 samples is at 15 kHz, which I can
hear, albeit weaker every year.

So, 3 points in time, separated by 1/44,100 of a second, with 15 bits
of resolution (plus the polarity bit). Can this really define any
sine wave accurately?

It only takes slightly more than two points to define a steady sine wave.

What about a decaying sine wave, one who's
amplitude is decreasing linearly or logarithmically with time?

That takes a set of points that defines a slightly decaying wave. They would
extend over the duration of the decaying wave. If the wave is decaying
slowly, that would be lots of points.

Can a mere 3 points really stay true to this, even without getting into
discussions of linearity of a DAC at -90 db.

Most DACs are actually quite linear at -90 dB, given a properly-dithered
signal.

This is my real interest in high frequency recordings. I don't
intend to go out and buy a super tweeter.

Been there, done that.

"Robert Morein" wrote in message

"Arny Krueger" wrote in message
...
"Robert Morein" wrote in message

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...



Since the sample rate has been stated to be 44.1 KHz, the
reconstruction filter needs to cut off slightly below 22.05 KHz, not
15 KHz. In the case of a 15 KHz signal, this gives a 7.05 KHz range
in which the filter needs to cut off.

Unfortunately, I misread the question.
Your mathematical analysis is basically correct.

However, your statement that the reconstruction filter problem has
been solved is not correct, and probably accounts for the small
variations in perceived quality among DACs.

Of course there are DACs that do sound different in time-synched,
level-matched, bias-controlled listening tests. And, there are DACs that
don't sound different in time-synched, level-matched, bias-controlled
listening tests.


A digital reconstruction filter cannot be perfect unless it has
infinite run length and is noncausal. While digital filters are
typically noncausal, they have limited run length.

Given that the ear is not absolutely perfect, there is no need for absolute
perfection in DACs.

Likewise for the analog filter. However, the run length of an analog
filter is even more severely restricted.

Usually the run length of a digital filter is related to its latency, and
latency is generally considered to be either bad or moot. Depends on the
application.

The reconstruction filter remains the weak link in DAC design.

Given that there are DACs that have zero reliable detectable effects on the
music they reproduce, even when the music is reproduced through them 5 or
more times, it is arguable that for the purpose of music listening, there
are no unsolved weak links in DAC design. AFAIK you have such a DAC in your
possession, and of course I think you should enjoy its excellent performance
by listening to as much music through it as possible.

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:VPVvb.4621$ML6.516@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show me the fourier series which contains only 15 kHz components
which results in a 15Khz waveform with "varying amplitude".

ScottW

On Sun, 23 Nov 2003 12:52:50 -0500, "Arny Krueger"
wrote:

Been there, done that.

Christ, you're putrid.

--
td

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:VPVvb.4621$ML6.516@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
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"Erik Squires" wrote in
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So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show a Fourier series with 15 Khz components that
results in an 15 kHz waveform of "varying amplitude"

ScottW

"ScottW" wrote in message
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"Arny Krueger" wrote in message
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"ScottW" wrote in message
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"Arny Krueger" wrote in message
...
"ScottW" wrote in message
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"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show me the fourier series which contains only 15 kHz components
which results in a 15Khz waveform with "varying amplitude".


A 15 KHz wave itself has varying amplitude. The amplitude varies at a rate
of 15 KHz.

"ScottW" wrote in message
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"Arny Krueger" wrote in message
...
"ScottW" wrote in message
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"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show a Fourier series with 15 Khz components that
results in an 15 kHz waveform of "varying amplitude"

Scotty, you must think this is one genius question, given that you asked it
twice. You're only getting one answer. Live with it!

On Sun, 23 Nov 2003 15:30:04 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
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"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:VPVvb.4621$ML6.516@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show me the fourier series which contains only 15 kHz components
which results in a 15Khz waveform with "varying amplitude".


A 15 KHz wave itself has varying amplitude. The amplitude varies at a rate
of 15 KHz.

You talk instantaneous values, him talk envelope. Waste time.

A 15 KHz wave itself has varying amplitude. The amplitude varies at a rate
of 15 KHz.


It seems pretty obvious to me he means varying peak amplitude with each cycle.

"Goofball_star_dot_etal" wrote in message

On Sun, 23 Nov 2003 15:30:04 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
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"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:VPVvb.4621$ML6.516@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples /
cycle.

Are the normal digital filters good enough to reproduce a 15
kHz signal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show me the Fourier series which contains only 15 kHz components
which results in a 15Khz waveform with "varying amplitude".


A 15 KHz wave itself has varying amplitude. The amplitude varies at
a rate of 15 KHz.

You talk instantaneous values, him talk envelope. Waste time.

That's his choice. If he wants a specific answer he should ask a specific
question.

"S888Wheel" wrote in message


A 15 KHz wave itself has varying amplitude. The amplitude varies at a
rate of 15 KHz.


It seems pretty obvious to me he means varying peak amplitude with
each cycle.

That's completely contrary to the context of the thread, which relates to
sample-by-sample amplitude.

I said


It seems pretty obvious to me he means varying peak amplitude with
each cycle.


Arny said


That's completely contrary to the context of the thread, which relates to
sample-by-sample amplitude.


It seems to me to be what Scott W. meant by varying amplitude. If that is what
he means, and I am confident it is what he means then it seems to me that it
will make a difference in how accurately one can plot a wave form using so few
samples per cycle. It also is the reality of music. Not a lot of sin waves with
no variation in peak amplitude in music. No doubt though, if one wants to
listen to sin waves with steady state peak amplitudes, digital should do a much
better job than analog.

"S888Wheel" wrote in message

I said


It seems pretty obvious to me he means varying peak amplitude with
each cycle.

Arny said

That's completely contrary to the context of the thread, which
relates to sample-by-sample amplitude.

It seems to me to be what Scott W. meant by varying amplitude.

Well, after he explained what he meant a second time, that is now pretty
clear.

Too bad he couldn't get it right the first time.

However, knowing what kind of buttholes you, Scottw and the rest of your
clique is sockpuppet Wheel, you're probably giving each other high fives
because you think he confounded me with his technical brilliance. The fact
of the matter is that he made a vague statement in a different context, and
I interpreted it in that context.

I said


It seems pretty obvious to me he means varying peak amplitude with
each cycle.




Arny said

That's completely contrary to the context of the thread, which
relates to sample-by-sample amplitude.


I said



It seems to me to be what Scott W. meant by varying amplitude.

Arny said



Well, after he explained what he meant a second time, that is now pretty
clear.

Too bad he couldn't get it right the first time.



I understood him the first time. Too bad you didn't.




However, knowing what kind of buttholes you, Scottw and the rest of your
clique is sockpuppet Wheel, you're probably giving each other high fives
because you think he confounded me with his technical brilliance.

Arny, didn't you get the message. Your sociopathic fantasies are boring. I have
never met Scott W. How the hell would I be giving him high-fives?

Arny said


The fact
of the matter is that he made a vague statement in a different context, and
I interpreted it in that context.


The fact of the matter is you didn't get what he was saying. When this happens
with normal people it is usually resolved with an explanation and no fecal
flinging. The fact that others including myself did get what he was saying
shows that part of the problem was your inability to figure out what was meant.

"S888Wheel" wrote in message


snip sockpuppet wheel's ranting about me being a sociopath

The fact
of the matter is that he made a vague statement in a different
context, and I interpreted it in that context.

The fact of the matter is you didn't get what he was saying.

It's not my fault he said it so badly. Scotty's inability to write coherent
English is like yours, well known.

When this happens with normal people it is usually resolved with an
explanation and no fecal flinging.

More examples of how you are crapping on this thread, sockpuppet Wheel. Just
for grins I held off on making any personal attacks so you could show how
low you can go.

The fact that others including
myself did get what he was saying shows that part of the problem was
your inability to figure out what was meant.

Thanks for showing once again sockpuppet wheel that you can't keep a civil
mouth in a technical thread.

Arny said


The fact
of the matter is that he made a vague statement in a different
context, and I interpreted it in that context.


I said



The fact of the matter is you didn't get what he was saying.


Arny said




It's not my fault he said it so badly.



If he said it so badly no one else would have understood his intent. Given the
fact that you were the only one who has claimed not to understand his intent
the logical conclusion is that your comprehension skills are sub par for RAO.

I said



When this happens with normal people it is usually resolved with an
explanation and no fecal flinging.



Arny said




More examples of how you are crapping on this thread,


Arny, I realize you have a limited imagination and, as you say yourself, you
are not the sharpest knife in the drawer but please at least try to come up
with an original idea. Stop plagiarizing me. Remember the shame it brought
Howard.

Arny said


Just
for grins I held off on making any personal attacks so you could show how
low you can go.


What a load of crap! Your posts are filled with personal attacks against Scott
W. over a ****ing misunderstanding between the two of you. Are you saying I
sank so low as to point out your malicious attacks against Scott W.? Wow!
That's pretty awful of me to call you on your personal attacks.


I said



The fact that others including
myself did get what he was saying shows that part of the problem was
your inability to figure out what was meant.

Arny said




Thanks for showing once again sockpuppet wheel that you can't keep a civil
mouth in a technical thread


Thanks for showing once again you have no clue when the issue is civility.

"S888Wheel" wrote in message


Thanks for showing once again you have no clue when the issue is
civility.

Yes, the issue is whose ox is being gored. In the end, your ox got gored
twice and now you're crying for momma again, sockpuppet wheel.

I said


Thanks for showing once again you have no clue when the issue is
civility.

Arny said


Yes, the issue is whose ox is being gored. In the end, your ox got gored
twice and now you're crying for momma again, sockpuppet wheel.



Stuck in another sociopathic fantasy again I see. Obviously your ability to
track the issues of a thread are in line with your self described intellect.
Should we call you butter-knife brain?

"Erik Squires" wrote in
ervers.com:

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude? How accurate is that signal, is there
no lag in the reconstructed signal? I mean, if the amplitude of the
original changes, is the reconstructed signal as true at 15 kHz as at
4 kHz?

This to me is a far more important concern than whether I can hear
20+kHz signals.

Thanks for your intelligent and well thought out replies. The rest of
you can suck my electric outlet.

Erik



First, with 44.1kHz sampling & 20-22kHz bandwidth a 15kHz signal can only
be a sine wave. Second, the 15kHz signal cannot be one isolated sine
wave, that would require more bandwidth. It will be a burst of waves with
a minimum buildup and decay. So it will be more than 3 samples of one
cycle. The closer the sine wave is to 22.05kHz the longer this build up
and decay must be to meet the bandwidth constraint.

Tim

--

"The strongest human instinct is to impart information,
and the second strongest is to resist it."

Kenneth Graham

"Browntimdc" wrote in message

"Erik Squires" wrote in
ervers.com:

So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.

Are the normal digital filters good enough to reproduce a 15 kHz
signal with varying amplitude? How accurate is that signal, is there
no lag in the reconstructed signal? I mean, if the amplitude of the
original changes, is the reconstructed signal as true at 15 kHz as at
4 kHz?

This to me is a far more important concern than whether I can hear
20+kHz signals.

Thanks for your intelligent and well thought out replies. The rest
of you can suck my electric outlet.

Erik



First, with 44.1kHz sampling & 20-22kHz bandwidth a 15kHz signal can
only be a sine wave.

Good point #1

Second, the 15kHz signal cannot be one isolated
sine wave, that would require more bandwidth. It will be a burst of
waves with a minimum buildup and decay. So it will be more than 3
samples of one cycle.

However, there need not ever be more than two samples per cycle, over
whatever period the sine wave actually extends.

The closer the sine wave is to 22.05kHz the
longer this build up and decay must be to meet the bandwidth
constraint.

A very observable effect. By the time one gets to 22.000 KHz, tone bursts
get pretty distorted. However, this is not a situation that is unique to the
digital domain. Same thing happens in the analog domain when the test
frequency is close to a sharp cut-off.

"Arny Krueger" wrote in message
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"Goofball_star_dot_etal" wrote in message

On Sun, 23 Nov 2003 15:30:04 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
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"Arny Krueger" wrote in message
...
"ScottW" wrote in message
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"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal, using a
44.1 kHz sampling rate, I'm going to get about 3 samples /
cycle.

Are the normal digital filters good enough to reproduce a 15
kHz signal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show me the Fourier series which contains only 15 kHz components
which results in a 15Khz waveform with "varying amplitude".


A 15 KHz wave itself has varying amplitude. The amplitude varies at
a rate of 15 KHz.

You talk instantaneous values, him talk envelope. Waste time.

That's his choice. If he wants a specific answer he should ask a specific
question.

Look at the original post.
Your context is wrong.
Too bad you gave the original poster such erroneous input.

ScottW

"ScottW" wrote in message
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"Arny Krueger" wrote in message
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"Goofball_star_dot_etal" wrote in message

On Sun, 23 Nov 2003 15:30:04 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:Wb7wb.4949$ML6.3520@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:VPVvb.4621$ML6.516@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal,
using a
44.1 kHz sampling rate, I'm going to get about 3 samples /
cycle.

Are the normal digital filters good enough to reproduce a 15
kHz signal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show me the Fourier series which contains only 15 kHz components
which results in a 15Khz waveform with "varying amplitude".


A 15 KHz wave itself has varying amplitude. The amplitude varies at
a rate of 15 KHz.

You talk instantaneous values, him talk envelope. Waste time.

That's his choice. If he wants a specific answer he should ask a
specific question.

Look at the original post.

I did.

Your context is wrong.

Wrong, the context wasn't set by me/ The problemis your comment is vague.

Too bad you gave the original poster such erroneous input.

Too bad you can't take responsibility for your own actions.

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
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"Arny Krueger" wrote in message
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"Goofball_star_dot_etal" wrote in message

On Sun, 23 Nov 2003 15:30:04 -0500, "Arny Krueger"
wrote:

"ScottW" wrote in message
news:Wb7wb.4949$ML6.3520@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:VPVvb.4621$ML6.516@fed1read01
"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:AmUvb.4608$ML6.2599@fed1read01
"Erik Squires" wrote in
message
ervers.com...

So, here's my question. If I digitize a 15 kHz signal,
using a
44.1 kHz sampling rate, I'm going to get about 3 samples /
cycle.

Are the normal digital filters good enough to reproduce a 15
kHz signal with varying amplitude?

Deconstruct this signal to frequency domain and it won't be a
pure 15 kHz.

Wrong.

What is the frequency of the amplitude "variation"?

Obviously, 15 KHz.

Show me the Fourier series which contains only 15 kHz components
which results in a 15Khz waveform with "varying amplitude".


A 15 KHz wave itself has varying amplitude. The amplitude varies at
a rate of 15 KHz.

You talk instantaneous values, him talk envelope. Waste time.

That's his choice. If he wants a specific answer he should ask a
specific question.

Look at the original post.

I did.

Your context is wrong.

Wrong, the context wasn't set by me/ The problemis your comment is vague.

BS, the context was set by the original poster when he specified a
signal with varying amplitude which has obvious implications.

Too bad you gave the original poster such erroneous input.

Too bad you can't take responsibility for your own actions.


Look at this paragraph dimwit and explain how your bs response
about instantaneous signal levels deals with "varying amplitude".

"Are the normal digital filters good enough to reproduce a 15 kHz singal
with
varying amplitude? "

You are wrong, again.

ScottW

"ScottW" wrote in message
news:ekEwb.6396$ML6.3958@fed1read01

Look at this paragraph dimwit and explain how your bs response
about instantaneous signal levels deals with "varying amplitude".

"Are the normal digital filters good enough to reproduce a 15 kHz
signal with varying amplitude? "

Since I now know Scotty that in your limited, fumbling way, you were trying
to describe a 15 KHz tone that is modulated, I can say quite clearly:

The answer is: Normal digital filters are plenty good enough to reproduce a
15 kHz signal with a varying amplitude of the kind actually seen with
music. For example if that 15 KHz signal is amplitude modulated with say 1
KHz, then there are sidebands at 14 KHz and 16 KHz. There's no problem
passing both the carrier at 15 KHz and the sidebands through a normal 44.1
KHz reconstruction filter which has a brick wall characteristic at 22.05 KHz

Notice that the proper way to ask the question involves the word
"modulated", or something like it.

If you wanted to make up a situation where normal 44.1 KHz reconstruction
filters significantly inhibit reproduction of a modulated tone, you'd pick a
much higher carrier frequency, such as 21.50 KHz, not 15 KHz.

My earlier answer:

"Three samples is sufficient to define a sine wave that has unique
frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient." still applies.

In the case of the 15 KHz sine wave modulated with 1 KHz, 44.1 KHz sampling
is adequate to handle the highest frequency that one finds in the Fourier
analysis of the signal, which is 16 KHz.

"Arny Krueger" wrote in message
...
"ScottW" wrote in message
news:ekEwb.6396$ML6.3958@fed1read01

Look at this paragraph dimwit and explain how your bs response
about instantaneous signal levels deals with "varying amplitude".

"Are the normal digital filters good enough to reproduce a 15 kHz
signal with varying amplitude? "

Since I now know Scotty that in your limited, fumbling way, you were
trying
to describe a 15 KHz tone that is modulated, I can say quite clearly:

The answer is: Normal digital filters are plenty good enough to reproduce
a
15 kHz signal with a varying amplitude of the kind actually seen with
music. For example if that 15 KHz signal is amplitude modulated with say
1
KHz, then there are sidebands at 14 KHz and 16 KHz. There's no problem
passing both the carrier at 15 KHz and the sidebands through a normal
44.1
KHz reconstruction filter which has a brick wall characteristic at 22.05
KHz


Thanks for admitting I was correct in my original post where I said:
"Deconstruct this signal to frequency domain and it won't be a pure
15 kHz."

To which you replied in error:
"Wrong."



Notice that the proper way to ask the question involves the word
"modulated", or something like it.

Then go bitch at the original poster. I don't know what you find so
complicated and incomprehensible about "varying amplitude"
but it really isn't. Maybe your general engineering cirriculum
wasn't all that comprehensive.

If you wanted to make up a situation where normal 44.1 KHz reconstruction
filters significantly inhibit reproduction of a modulated tone, you'd
pick a
much higher carrier frequency, such as 21.50 KHz, not 15 KHz.

My earlier answer:

"Three samples is sufficient to define a sine wave that has unique
frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient." still applies.

In the case of the 15 KHz sine wave modulated with 1 KHz, 44.1 KHz
sampling
is adequate to handle the highest frequency that one finds in the Fourier
analysis of the signal, which is 16 KHz.

None of which changes the relevance of my original response to which you
replied in
error. Thank you for finally admitting the truth.

ScottW