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Industrial One · Guest

Most audio files on the net are recorded at a 44 KHz sampling rate,
but it>s mainly referred as "frequency." Now, humans can only hear up
to 20 KHz, so why would audio be recorded at 44 KHz (twice the audible
hearing range?) Obviously, one can notice the difference if the song
was downsampled to 22, so why not coin the standard frequency at 22
KHz instead of 44, why is the number doubled? Also, just where the
hell did the number 44,100 emerge from? Why not 40,000?

Nowadays, DVD-audio songs are recorded at 96/192 KHz, is there a
point?

And if this ain>t the case, why would the sampling rate be called
"frequency?"

Earl Kiosterud · Guest

"Industrial One" <industrial_one@hotmail.com> wrote in message
news:591b3f55-e2e1-408e-8b84-d8e8016cb452@z72g2000hsb.googlegroups.com...
[quote]Most audio files on the net are recorded at a 44 KHz sampling rate,
but it>s mainly referred as "frequency." Now, humans can only hear up
to 20 KHz, so why would audio be recorded at 44 KHz (twice the audible
hearing range?) Obviously, one can notice the difference if the song
was downsampled to 22, so why not coin the standard frequency at 22
KHz instead of 44, why is the number doubled? Also, just where the
hell did the number 44,100 emerge from? Why not 40,000?

Nowadays, DVD-audio songs are recorded at 96/192 KHz, is there a
point?

And if this ain>t the case, why would the sampling rate be called
"frequency?"
[/quote]
Sampling theory tells us that it takes at least two samples per cycle, hence the 44.1 KHz
sample rate. The highest frequency that can be captured is 22.05 KHz (Nyquist frequency);
frequencies higher than that will create alias frequencies below 22.05 For example, an
audio frequency at 30 KHz would produce an alias frequency component at 14.1 KHz (44.1 -
30). It also produces one at 44.1 + 30, but who cares? The 20KHz audio upper limit allows
for comfortable guard band to the Nyquist frequency.

DVD audio is just for marketing. No one, with the possible exception of a few young people
who can hear above 20 KHz, and many dogs, can hear the difference between regular 44.1K
16-bit audio and 96 or 192K sampling and 24 bits -- it>s been proven, though some will tell
you they can. It>s something they call "resolution" for which they have an altar, dogma and
lots of ritual. They get this dreamy look in their eyes. Challenge it, and their veins pop
out and they go on rampages. It>s likely that much of the stuff you get on DVD-audio discs
is better stuff, and has been more meticulously recorded, hence the good sound of many of
them. It ain>t the extravagant bit depth and sampling rate. There are some damned
good-sounding CDs too. Even if you had a regular CD version and a DVD-audio version, and
the DVD-audio version sounded better, would you actually believe that the improvement was
because of the bit depth and sample rate? Couldn>t be anything else, could it? How are
they going to sell DVD-audio discs if they let the CDs sound the same?

Hope this helps.
--
Earl

Richard Crowley · Guest

"Industrial One" wrote ...
[quote]Most audio files on the net are recorded at a 44 KHz sampling rate,
[/quote]
The "Red Book" convention for making audio CDs was developed
back in the early 1980s and established 44.1KHz as the sampling
rate. In order to maintain forwards and backwards compatibility,
all CDs must use that sample rate.

[quote]but it>s mainly referred as "frequency."
[/quote]
Any periodic occurance can be referred to as "freqency". Whether
it is something that happens every femtosecond (like light) or every
1000 years (like the century).

[quote]Now, humans can only hear up to 20 KHz, so why would audio be
recorded at 44 KHz (twice the audible hearing range?)
so why not coin the standard frequency at 22
KHz instead of 44, why is the number doubled?
[/quote]
The Nyquist-Shannon sampling therom tells us that you must
sample at *twice* the desired highest frequency to adequately
reproduce the original waveform. It is said that 22KHz was
selected as the top end (x2 = 44KHz) because of the state of
the art in filters back in those days.

[quote]Obviously, one can notice the difference if the song was
downsampled to 22,
[/quote]
You notice it because reducing the sampling rate to 22KHz
actually reduces the top end to 11KHz which many people
can detect.

http://en.wikipedia.org/wiki/Compact_disc
http://en.wikipedia.org/wiki/Red_Book_%28audio_CD_standard%29
http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

[quote]Also, just where the hell did the number 44,100 emerge from?
Why not 40,000?
[/quote]
It is said that 22KHz was selected as the top end to give some
space between the theoretical maximum "hi-fi" frequency of 20KHz
and the filter frequency (22KHz to allow room for the slope of the
filter. Modern techniques make most of the original parameters moot.

[quote]Nowadays, DVD-audio songs are recorded at 96/192 KHz, is
there a point?
[/quote]
No.

[quote]And if this ain>t the case, why would the sampling rate be called
"frequency?"
[/quote]
Any periodic occurrence can be referred to as "frequency". Whether
it is something that happens every femtosecond (like light) or every
1000 years (like a new century). Most of us have to pay for electricity
and our billing cycle happens with a frequency of one month. This is
common scientific/engineering terminology. No great mystery.

Mr.T · Guest

"Richard Crowley" <rcrowley@xp7rt.net> wrote in message
news:5u-dnb_XvbVZxe3VnZ2dnUVZ8trinZ2d@posted.pcez...
[quote]Any periodic occurance can be referred to as "freqency". Whether
it is something that happens every femtosecond (like light) or every
1000 years (like the century).
[/quote]
Only *one* century every thousand years where you live?

<Snip>
[quote]Any periodic occurrence can be referred to as "frequency". Whether
it is something that happens every femtosecond (like light) or every
1000 years (like a new century).
[/quote]
Obviously not a typo then.

MrT.

Edmund · Guest

On Sun, 06 Jul 2008 04:18:32 +0000, Earl Kiosterud wrote:

[quote]"Industrial One" <industrial_one@hotmail.com> wrote in message
news:591b3f55-e2e1-408e-8b84-
d8e8016cb452@z72g2000hsb.googlegroups.com...
Most audio files on the net are recorded at a 44 KHz sampling rate, but
it>s mainly referred as "frequency." Now, humans can only hear up to 20
KHz, so why would audio be recorded at 44 KHz (twice the audible
hearing range?) Obviously, one can notice the difference if the song
was downsampled to 22, so why not coin the standard frequency at 22 KHz
instead of 44, why is the number doubled? Also, just where the hell did
the number 44,100 emerge from? Why not 40,000?

Nowadays, DVD-audio songs are recorded at 96/192 KHz, is there a point?

And if this ain>t the case, why would the sampling rate be called
"frequency?"

Sampling theory tells us that it takes at least two samples per cycle,
hence the 44.1 KHz sample rate. The highest frequency that can be
captured is 22.05 KHz (Nyquist frequency); frequencies higher than that
will create alias frequencies below 22.05 For example, an audio
frequency at 30 KHz would produce an alias frequency component at 14.1
KHz (44.1 - 30). It also produces one at 44.1 + 30, but who cares? The
20KHz audio upper limit allows for comfortable guard band to the Nyquist
frequency.

DVD audio is just for marketing. No one, with the possible exception of
a few young people who can hear above 20 KHz, and many dogs, can hear
the difference between regular 44.1K 16-bit audio and 96 or 192K
sampling and 24 bits -- it>s been proven, though some will tell you they
can.
[/quote]
I heard about that tests and it was criticized because the music was
played over a pair of passive loudspeakers with passive filters that
where nowhere near phase linear same problem with electrostatic
speakers with step up transformers . So no matter how much better
SACD or DVDA can be, played over such loudspeakers all the
advantages are down the drain.
Don>t know if this story is true but I very much like to attend such
a listening test an judge for myself.
Did anyone here did attend such a test and on what kind of speakers
was it played?

Edmund

Chronic Philharmonic · Guest

"Industrial One" <industrial_one@hotmail.com> wrote in message
news:591b3f55-e2e1-408e-8b84-d8e8016cb452@z72g2000hsb.googlegroups.com...
[quote]Most audio files on the net are recorded at a 44 KHz sampling rate,
but it>s mainly referred as "frequency." Now, humans can only hear up
to 20 KHz, so why would audio be recorded at 44 KHz (twice the audible
hearing range?) Obviously, one can notice the difference if the song
was downsampled to 22, so why not coin the standard frequency at 22
KHz instead of 44, why is the number doubled? Also, just where the
hell did the number 44,100 emerge from? Why not 40,000?
[/quote]
It was because they used video recorders for mastering prototype and first
generation CDs, and it was the nearest available frequency that was greater
than 40KHz needed to meet the sampling Nyquist requirement of at least two
samples for the highest frequency to be recorded (20KHz). See also:
http://www.cs.columbia.edu/~hgs/audio/44.1.html

[quote]Nowadays, DVD-audio songs are recorded at 96/192 KHz, is there a
point?
[/quote]
Marketing. There is no defensible mathematical requirement for it.

[quote]And if this ain>t the case, why would the sampling rate be called
"frequency?"
[/quote]
The sampling rate is a frequency. CD audio is sampled at a frequency of
44.1KHz.

John Phillips · Guest

On 2008-07-06, Edmund <nomail@hotmail.com> wrote:
[quote]On Sun, 06 Jul 2008 04:18:32 +0000, Earl Kiosterud wrote:
DVD audio is just for marketing. No one, with the possible exception of
a few young people who can hear above 20 KHz, and many dogs, can hear
the difference between regular 44.1K 16-bit audio and 96 or 192K
sampling and 24 bits -- it>s been proven, though some will tell you they
can.

I heard about that tests and it was criticized because the music was
played over a pair of passive loudspeakers with passive filters that
where nowhere near phase linear same problem with electrostatic
speakers with step up transformers . So no matter how much better
SACD or DVDA can be, played over such loudspeakers all the
advantages are down the drain.
[/quote]
I assume this refers to the Meyer & Moran paper in JAES (see
http://www.aes.org/e-lib/browse.cfm?elib=14195). If so, I understand
it was conducted over a number of different "high-res" systems but each
test using the same 44.1 kHz/16 bit A/D - D/A loop. For example here>s
a subsequent comment from E. Brad Meyer:

"... But it was a near certainty that someone in that part of the
industry would claim that with a 'real audiophile system' the
differences would have been obvious. So we found such a system and
gave its owner and his friends a chance. We conducted that test
with the same rigor as the others; levels of the two signals
were matched within 0.1 dB at 1 kHz, and then the subjects were
asked to choose their best material and listen however they usually
do, to maximize their aural acuity."

--
John Phillips

Arny Krueger · Guest

"Edmund" <nomail@hotmail.com> wrote in message
news:48708734$0$17237$bf4948fe@news.tele2.nl

[quote]I heard about that tests and it was criticized because
the music was played over a pair of passive loudspeakers
with passive filters that where nowhere near phase linear
[/quote]
As a rule, speakers are nowhere near phase linear, regardless of the
implementation of the crossover.

However, similar tests have been done with transducers that have better
phase response, and same results.

Furthermore, you are ignoring the fact that linear phase microphones are
only a little bit easier to find, and as a rule they are not used to record
music.

[quote]same problem with electrostatic speakers with step up
transformers .
[/quote]
Same problem with 99,9% (more or less) of all loudspeakers ever made.

So what?

[quote]So no matter how much better SACD or DVDA
can be, played over such loudspeakers all the advantages
are down the drain.
[/quote]
Even if you were right, you>re basically admitting that SACD and DVDA have
no real world application.

[quote]Don>t know if this story is true but I very much like to
attend such a listening test an judge for myself.
[/quote]
I doubt that, the tests are blind tests.

[quote]Did anyone here did attend such a test and on what kind
of speakers was it played?
[/quote]
I can guarantee you that they weren>t phase linear.

cr88192 · Guest

"Industrial One" <industrial_one@hotmail.com> wrote in message
news:591b3f55-e2e1-408e-8b84-d8e8016cb452@z72g2000hsb.googlegroups.com...
[quote]Most audio files on the net are recorded at a 44 KHz sampling rate,
but it>s mainly referred as "frequency." Now, humans can only hear up
to 20 KHz, so why would audio be recorded at 44 KHz (twice the audible
hearing range?) Obviously, one can notice the difference if the song
was downsampled to 22, so why not coin the standard frequency at 22
KHz instead of 44, why is the number doubled? Also, just where the
hell did the number 44,100 emerge from? Why not 40,000?

[/quote]
as others have noted...

[quote]Nowadays, DVD-audio songs are recorded at 96/192 KHz, is there a
point?

[/quote]
not really for listening as least, but for "audio as data", higher sampling
rate and bit depth makes sense.
of course, it is rather unlikely that end users would be doing the levels of
processing (notable doppler shifting, signal analysis, ...) that would
justify this. of course, in my case, I am usually dealing with lower-quality
input, so it works fairly well to just use 44.1kHz 16-bits anyways (one gets
a better payoff trying to write good quality filtering functions).

likewise, IMO, for MP3s much above about 128 or 192 kbps, I don>t personally
hear any real difference (actually, for internet radio at least, I prefer a
little lower bitrates, as at least then the stream has less stalling and
buffering issues).

for something unrelated it is a thought that, for "audio as data" uses, one
could stuff a little bit higher-range data into the 16-bit samples, by
representing a slightly bigger range (say, 24 bits), as log-scaled values
within the 16 bit range. of course, this would likely reduce quality a
little, and add a little noise, if played back as 16 bit audio (mostly,
really quiet stuff that would normally be quantized away is left).

log10(8388608)=6.9236899, log10(32768)=4.51545
6.9236899/4.51545=1.53333333
....

actually, recently I have been suspecting that, mathematically (and for a
defined dynamic range) log-scaled values may be much more accurate for a
given number of bits than an actual floating-point format (in particular, I
think that splitting the mantissa and exponent wastes some amount of the
value range).

of course, a claim like this would require testing, and even then, who would
really care?...

it only really makes that much difference for 24 bits and lower (where
FP-style encoding starts breaking down anyways). yes, the accuracy of 16-bit
half-floats suck, not much debate here. I guess the question is if log-scale
values would be more accurate when covering the same range (2^16 to 2^-16).

it may have practical relevance though, since log-scale values are quicker
and easier to encode and decode than hfloats (given modern HW tends not to
support them anyways).

would still need to be verified though.

[quote]And if this ain>t the case, why would the sampling rate be called
"frequency?"
[/quote]
as others have noted.

police also buy doughnuts with a high frequency...
doesn>t mean they are chirping at the cashier...

Guest · Posted: Sun Jul 06, 2008 8:45 pm Post subject: Re: Frequency/Sample rate

On Jul 5, 11:47 pm, Industrial One <industrial_...@hotmail.com> wrote:
[quote]Most audio files on the net are recorded at a 44 KHz sampling rate,
but it>s mainly referred as "frequency." Now, humans can only hear up
to 20 KHz, so why would audio be recorded at 44 KHz (twice the audible
hearing range?)
[/quote]
Others have chimed in (regretably, some incorrectly), but
the short answer is: the nathematical basis behind periodic
sampling tells us that if we have a singnal whose bandwidth
is, oh, "x", to capture that sample that signal with no loss of
time-domain information or have no unwanted artifacts, we
are required to sampke that signal at MORE THAN twice "x".

For example, if you assume the bandwidth of human
hearing is 20 kHz, you must sample at more than
2*20 kHz or GREATER THAN 40 kHz to ensure that
everything within that 20 kHz bandwidth is captured
and not lost.

One of the MOST important parts of a properly implemented
sampler is the preceeding band-limiting filter. ALL operational
sampler (no exceptions) provide some means of ensureing
that NO components outside that bandwidth reach the sampler.

What it comes down to is this: IF you can assume, a priori,
that your bandwidth is LESS THAN 1/2 the sampling rate,
ALL waveforms within that bandwidth can and are uniquely
identified by all available samples. If you have, say, 2.0001
samples per cycle of, say, a sine wave, there is exactly one
and ONLY one waveform whose bandwidth is less than
1.2 the sample rate that can pass through those samples.

Adding more samples will NOT make the representation
of that waveform ANY more precise: it will simply waste data.

[quote]Obviously, one can notice the difference if the song
was downsampled to 22, so why not coin the standard
frequency at 22 KHz instead of 44, why is the number
doubled?
[/quote]
Because, if you follow the discussion about the requirements
of a sampler, when you have down-sampled to 22 kHz, you
have to first filter EVERYTHING that>s at or above half that,
or 11 kHz. And many people have no problem hearing the
intrusion of a <11kHz low pass filter on the right kind of
musical material.

And, to repeat, it>s not doubled, it>s multiplied by SLIGHTLY
more than double.

[quote]Also, just where the
hell did the number 44,100 emerge from? Why not 40,000?
[/quote]
Way back in the late 1970>s, the only form of portable
recordable storage that was affordable for the kind of data
rates needed for digital audio were video tape recorders.
The samplers used the vertical modulation from white to
black to store 1>s and 0>s. To ease the designof the samplers
and the synchronization and to meet the bandwidth limts
of the recorders, it was decide to put an intergral number
of samples on each scan line.

For 60 Hz/525 line NTSC, you have 35 blanked lines, leaving
490 lines per frame, 245 line for field. Storing 3 samples per
line, the resulting sample rate becomes:

60 field/second * 245 lines/field * 3 samples/line =

44.1 kHz samples per second. Similar calculations yield
sample rates of 48 kS/s and 50 Hz/625 PAL video can also
accomodate these rates in similar fashions.

One very interesting side benefit is not only could you
store wide-band audio this way, you could also transmit
the resulting digitized audio over normal broadcast TV
channels with no loss. During the '80s' a number of stations
did just that: if you had a compatible D/A converter, you
could listen to full bandwidth digital audio at home from your
TV set.

[quote]Nowadays, DVD-audio songs are recorded at 96/192 KHz, is there a
point?

And if this ain>t the case, why would the sampling rate be called
"frequency?"
[/quote]
Becasue "frequency, in the technical parlance, means quite
precisely "per unit time" Whether it>s cycles per second or
sample per second or high tides per day, they all describe
the frequency, or how often, at which some semi-periodic
event happens.

Randy Yates · Guest

Industrial One <industrial_one@hotmail.com> writes:

[quote]Most audio files on the net are recorded at a 44 KHz sampling rate,
but it>s mainly referred as "frequency." Now, humans can only hear up
to 20 KHz, so why would audio be recorded at 44 KHz (twice the audible
hearing range?) Obviously, one can notice the difference if the song
was downsampled to 22, so why not coin the standard frequency at 22
KHz instead of 44, why is the number doubled?
[/quote]
What you>re missing is that the bandwidth of a digital system is
HALF the sample rate. So sampling at 44.1 kHz passes (potentially)
a signal with frequencies up to 22.05 kHz.

[quote]Also, just where the hell did the number 44,100 emerge from? Why not
40,000?
[/quote]
See 44,100 and 44,056 here:

http://en.wikipedia.org/wiki/Sampling_rate

[quote]Nowadays, DVD-audio songs are recorded at 96/192 KHz, is there a
point?
[/quote]
Yes - to make Sony and other media moguls more money (by requiring
people to replace their collections). Other than that, no.

[quote]And if this ain>t the case, why would the sampling rate be called
"frequency?"
[/quote]
Simple laziness - humans get lazy with terms.
--
% Randy Yates % "Ticket to the moon, flight leaves here today
%% Fuquay-Varina, NC % from Satellite 2"
%%% 919-577-9882 % 'Ticket To The Moon'
%%%% <yates@ieee.org> % *Time*, Electric Light Orchestra
http://www.digitalsignallabs.com

Chronic Philharmonic · Guest

"Randy Yates" <yates@ieee.org> wrote in message
news:m3lk0esb2y.fsf@ieee.org...
[quote]Industrial One <industrial_one@hotmail.com> writes:
[/quote]
[snip]

[quote]And if this ain>t the case, why would the sampling rate be called
"frequency?"

Simple laziness - humans get lazy with terms.
[/quote]
I do not think the term frequency is being used improperly. A sample rate
has a frequency:

Q: "How frequently are you sampling?"
A: "44.1 thousand times a second -- at a frequency of 44.1KHz"

Guest · Posted: Mon Jul 07, 2008 9:01 am Post subject: Re: Frequency/Sample rate

To take a contrarian position here:

Here is a good article for understanding sampling theory:
http://www.wescottdesign.com/articles/Sampling/sampling.html

When you sample a signal, you have to tradeoff between frequency
response, aliasing, and ringing artifacts. For audio I believe it>s
ok to have ringing since we don>t notice it.

On reproducing that signal, there is that set of tradeoffs a second
time. So you can lose frequency response there again.

In practical systems, you aren>t working with idealized sinc filters
(brickwall) so there is some dropoff in frequency response when you
sample that signal and again when you reproduce it as sound. So
depending on what analog filters cost, etc. etc. there might be some
sense in going with 96khz systems. It definitely does make sense to
sample at 96khz at acquisition... the oversampling is beneficial (if
you sample at 48khz, you can>t get very good frequency response
because the analog filters won>t let you do that).

2- Anyways this is just speculating. The real way to figure it out is
to do a test. Unfortunately I haven>t done so myself. But according
to one audio engineer, there is an audible difference. So maybe there
is merit to 96khz systems. Do read the sampling article as it
provides a better understanding of what goes on.

http://www.prorec.com/Articles/tabid/109/EntryId/158/Default.aspx

QUOTE:

I know... I know... I can hear many of you saying there is absolutely
NO need for recording with a 96kHZ Sample Rate. Two weeks ago, I would
have agreed with you! I emphasize *would have* agreed with you! Let me
state this very clearly... YOU CAN INDEED HEAR THE DIFFERENCE when
recording with a 96kHz Sample Rate!

I wouldn>t have believed it myself if I hadn>t heard the results.
Bottom line is that the highs sound more open and detailed. By the
way... two other folks here in my studio could pick the 96kHz track
EVERY time in a blind listening test (when compared with a 44.1kHz
version). To hell with theory, my EARS tell me there is a difference.

Want a real dose of Blasphemy? I compared recording at 96kHz and
Sample Rate converting down to 44.1, to simply recording at 44.1kHz. I
couldn>t believe my ears! The track originally recorded at 96kHz and
Sample Rate converted down to 44.1kHz had much better sounding highs,
maintaining much of the character from recording at 96kHz.

This goes against everything that I have learned over the years... and
goes against accepted practice. So I don>t make this statement
lightly! You CAN hear a difference... anyone who tells you otherwise
hasn>t tried recording at 96kHz! Period.

Pasi Ojala · Guest

On 2008-07-07, glennchan@gmail.com <glennchan@gmail.com> wrote:
[quote]When you sample a signal, you have to tradeoff between frequency
response, aliasing, and ringing artifacts. For audio I believe it>s
ok to have ringing since we don>t notice it.
[/quote]
Ringing is not an artifact, it is how a band-limited signal
behaves. It may look funny on the computer screen, but you don>t
hear it because there is nothing wrong with it in the first place.

Take a square wave for example. You can create that as a digital
signal "easily", by taking a base-frequency sine and all of the
odd multiplies with the proper gains. Continue into infinity and
you have a nice square wave. Stop at the band edge and you get
"ringing". But it really isn>t an artifact, you have all the
sines intact that you added.

[quote]On reproducing that signal, there is that set of tradeoffs a second
time. So you can lose frequency response there again.
[/quote]
You can lose bandwidth, but there is enough information to
perfectly generate the signal that was properly low-pass
filtered at the sampling end.

[quote]depending on what analog filters cost, etc. etc. there might be some
sense in going with 96khz systems. It definitely does make sense to
sample at 96khz at acquisition... the oversampling is beneficial
[/quote]
Analog filters have not been used for years. You digitally
upsample and filter to get a DAC frequency of for example 6MHz,
then use a first-order lowpass to filter above for example 100kHz.
There is no need to use 96kHz samplerate.

[quote]To hell with theory, my EARS tell me there is a difference.
[/quote]
Everything else being equal you can>t hear frequencies above
22kHz. So obviously everything else has not been equal.

-Pasi
--
"I know, I know what it>s like to lose someone, only to find her and
then lose her a second time. I wouldn>t wish that on anyone, not even
you, as much as I might want to."
-- Sheridan to Bester in Babylon 5:"Rising Star"

Guest · Posted: Mon Jul 07, 2008 12:50 pm Post subject: Re: Frequency/Sample rate

On Jul 7, 5:01 am, glennc...@gmail.com wrote:
[quote]When you sample a signal, you have to tradeoff between frequency
response, aliasing, and ringing artifacts. For audio I believe it>s
ok to have ringing since we don>t notice it.
[/quote]
A fundamental error here.

First, sampling does not cause the "ringing," it>s the
truncation of the bandwidth. You can have all sorts of
ringing in a continuous time analog system. Look at the
output, for example, of an old-style analog anti-aliasing
filter that preceeded early generation A/D converters.

Take a 1 kHz square wave. Band limit it with a 20 kHz
low-bass filter.

Now, sum the following series:

F(t) = sum (sin(x*t)/x) where x = 2 pi * 1, 3, 5, ... 19

and see what you get. Is the ringing in the first case real
and in the second case simply a result of truncation of
a mathematical series?

[quote]On reproducing that signal, there is that set of tradeoffs a second
time. So you can lose frequency response there again.
[/quote]
Why? How? I have inexpensive A/D and D/A chains here
that have frequency response from 2 Hz to 20 kHz with less
than +-.2 dB total error across the band and with a phase
response 20-20 kHz with 5 degrees or 0.

What "lost frequency response" are you talking about?

[quote]In practical systems, you aren>t working with idealized sinc filters
(brickwall) so there is some dropoff in frequency response when you
sample that signal and again when you reproduce it as sound.
[/quote]
I don>t sample it again and again when I reproduce it.

[quote]So depending on what analog filters cost, etc. etc. there
might be some sense in going with 96khz systems.
[/quote]
The analog filter in the BEST 44.1 kHz digital system I have
here costs on the order of a buck or two and has almost
NO imact whatsoever on the frequency response within
the 20 kHz audio bandwidth.

[quote]It definitely does make sense to
sample at 96khz at acquisition... the oversampling is beneficial (if
you sample at 48khz, you can>t get very good frequency response
because the analog filters won>t let you do that).
[/quote]
That>s why NO ONE uses analog filters to do this job.
THat>s why no one with any competence has used analog
anti-aliasing and anti-imaging filters for two decades.

And what you>re talkig about is NOT "oversampling."

In fact, for the last two decades, MOSTY A/D and D/A
systems HAVE used oversampling techniques to
elininate the issues surrounding analog filters. And the
run not at 96 kHz or 192, but are 44.1 or 48 kHz oversampled
systems.

[quote]2- Anyways this is just speculating. The real way to figure it out is
to do a test. Unfortunately I haven>t done so myself. But according
to one audio engineer, there is an audible difference.
[/quote]
And, according to many independent researchers, there is not.


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