Theoretically Highest Quality of PCM Audio

What is the theoretically highest possible:

1. Frequency Response (range of frequencies)

2. SNR

3. Dynamic Range

4. SPL

5. Musical Pitch (highest acceptable frequency)

of PCM audio?

On Sun, 09 Nov 2003 14:45:19 -0800, Radium wrote:

> What is the theoretically highest possible:

Based on what theory?  Based on what PCM audio?  Red Book?  DVD-A?
Some arbitrary, non-standard interconnect?  The main system bus of a
computer that processes said PCM audio?

Since one can (and does) use PCM at all levels and scales of physical
analysis (electron microscopy, earthquake analysis, radar, etc), then the
limitations are going to come from what you define to be "audio", in the
context of "PCM audio".

Once you define your terms, the answers to all of your questions can be
simply derived.

> 1. Frequency Response (range of frequencies)
> 
> 2. SNR
> 
> 3. Dynamic Range
> 
> 4. SPL
> 
> 5. Musical Pitch (highest acceptable frequency)
> 
> of PCM audio?

-- 
Andrew

Radium wrote:
> 
> What is the theoretically highest possible:
> 
> 1. Frequency Response (range of frequencies)
> 
> 2. SNR
> 
> 3. Dynamic Range
> 
> 4. SPL
> 
> 5. Musical Pitch (highest acceptable frequency)
> 
> of PCM audio?

Google up "Shannon Theorem". 

--
Les Cargill

In article 3FAED264.DC692FE1@worldnet.att.net, Les Cargill at
lcargill@worldnet.att.net wrote on 11/09/2003 18:47:

> Radium wrote:
>> 
>> What is the theoretically highest possible:
>> 
>> 1. Frequency Response (range of frequencies)

DC to just under 1/2 of the sampling frequency (what we normally call the
"Nyquist Frequency").

>> 2. SNR
>> 
>> 3. Dynamic Range


depends on what kind of "S" that is being compared to what kind of "N".  if
the assumption is that S and N have the same kind of qualitative statistics
(say, both having uniform p.d.f.), then the SNR in dB + dB of headroom
(which is what i would normally think is dB of dynamic range) is 6.02 dB per
bit of PCM word width.

>> 4. SPL

depends on how high you crank up your volume knob.  has nothing to do with
PCM or whatever else the audio is.

>> 5. Musical Pitch (highest acceptable frequency)

theoretically, just below the Nyquist frequency divided by the index of the
highest harmonic of the musical note.

>> of PCM audio?
> 
> Google up "Shannon Theorem".

good advice, Les.  also maybe Google "Shannon Information Theory" to get the
low-down on bits vs. dB.

r b-j

Andrew Reilly <andrew@gurney.reilly.home> wrote in message news:<pan.2003.11.09.23.10.59.63234@gurney.reilly.home>...
> On Sun, 09 Nov 2003 14:45:19 -0800, Radium wrote:
> 
> > What is the theoretically highest possible:
> 
> Based on what theory?  Based on what PCM audio?  Red Book?  DVD-A?
> Some arbitrary, non-standard interconnect?  The main system bus of a
> computer that processes said PCM audio?
> 
> Since one can (and does) use PCM at all levels and scales of physical
> analysis (electron microscopy, earthquake analysis, radar, etc), then the
> limitations are going to come from what you define to be "audio", in the
> context of "PCM audio".
> 
> Once you define your terms, the answers to all of your questions can be
> simply derived.

Sorry, but he DID define his terms. "PCM audio," meaning "pulse
code modulation audio" is sufficiently unambiguous to answer
his question. We don't have to know DVD, red book or anything
else.

> > 1. Frequency Response (range of frequencies)

The maximum bandwidth possible without the introduction of
unwanted artifacts must be less than 1/2 the sampling rate.

> > 2. SNR
> > 3. Dynamic Range

The two are equivalent when the signal is the maximum undistorted
signal the medium can accept. In such a case, the dynamic range,
as defined as the ratio between the smallest unmabiguously encodable
sample measured over the bandwidth of the system and the maximum
undistorted signal is approximately 6.02 dB per bit.

> > 4. SPL

Sorry, SPL is irrelevant, because it includes factors not relevant
to the PCM process, such as amplifier gain, loudspeaker efficiency,
distance from the speaker, and any other factors that has nothing
to do with "PCM"

> > 5. Musical Pitch (highest acceptable frequency)

Sorry, but this is a case where your use of the terminology is murky.
"pitch" is defined as the psychoacoustic perception as it relates
to the frequency of a tone. As to the highest possible frequency,
assuming base-band usage, is simply less than 1/2 the sampling rate.

Andrew Reilly <andrew@gurney.reilly.home> wrote in message news:<pan.2003.11.09.23.10.59.63234@gurney.reilly.home>...
> On Sun, 09 Nov 2003 14:45:19 -0800, Radium wrote:
> 
> > What is the theoretically highest possible:
> 
> Based on what theory?  

Sampling rate = 2(highest frequency)

Bit resolution = dynamic range/2

bytes per second = information per time

The high sample rate and bit resolution the better the audio quality.

The shortest amount of time is 10^-43 second. What is the maximum # of
bits that can squeezed into this sml amt of time?

dpierce@cartchunk.org (Dick Pierce) writes:

> Andrew Reilly <andrew@gurney.reilly.home> wrote in message news:<pan.2003.11.09.23.10.59.63234@gurney.reilly.home>...
> > On Sun, 09 Nov 2003 14:45:19 -0800, Radium wrote:
> > 
> > > What is the theoretically highest possible:
> > 
> > Based on what theory?  Based on what PCM audio?  Red Book?  DVD-A?
> > Some arbitrary, non-standard interconnect?  The main system bus of a
> > computer that processes said PCM audio?
> > 
> > Since one can (and does) use PCM at all levels and scales of physical
> > analysis (electron microscopy, earthquake analysis, radar, etc), then the
> > limitations are going to come from what you define to be "audio", in the
> > context of "PCM audio".
> > 
> > Once you define your terms, the answers to all of your questions can be
> > simply derived.
> 
> Sorry, but he DID define his terms. "PCM audio," meaning "pulse
> code modulation audio" is sufficiently unambiguous to answer
> his question. We don't have to know DVD, red book or anything
> else.
> 
> > > 1. Frequency Response (range of frequencies)
> 
> The maximum bandwidth possible without the introduction of
> unwanted artifacts must be less than 1/2 the sampling rate.

He doesn't seem to have defined it well enough for you to give him a
precise answer.

> > > 2. SNR
> > > 3. Dynamic Range
> 
> The two are equivalent when the signal is the maximum undistorted
> signal the medium can accept. In such a case, the dynamic range,
> as defined as the ratio between the smallest unmabiguously encodable
> sample measured over the bandwidth of the system and the maximum
> undistorted signal is approximately 6.02 dB per bit.

Again, you appear to have to infer definitions, so perhaps the
original poster was not precise enough.

> > > 4. SPL
> 
> Sorry, SPL is irrelevant, because it includes factors not relevant
> to the PCM process, such as amplifier gain, loudspeaker efficiency,
> distance from the speaker, and any other factors that has nothing
> to do with "PCM"
> 
> > > 5. Musical Pitch (highest acceptable frequency)
> 
> Sorry, but this is a case where your use of the terminology is murky.
> "pitch" is defined as the psychoacoustic perception as it relates
> to the frequency of a tone. As to the highest possible frequency,
> assuming base-band usage, is simply less than 1/2 the sampling rate.

-- 
Peter J. Kootsookos

"I will ignore all ideas for new works [..], the invention of which
 has reached its limits and for whose improvement I see no further
 hope."

- Julius Frontinus, c. AD 84

On 9 Nov 2003 13:45:19 -0800, glucegen@excite.com (Radium) wrote:

>What is the theoretically highest possible:
>
>1. Frequency Response (range of frequencies)
>
>2. SNR
>
>3. Dynamic Range
>
>4. SPL
>
>5. Musical Pitch (highest acceptable frequency)
>
>of PCM audio?

There are no inherent limits, the current state of the art is 24/192.
This gives theoretical limits of 141dB SNR, which is the same as
dynamic range, and 0.0001Hz to 95kHz frequency response, with 95kHz of
course being the upper limit.

-- 

Stewart Pinkerton | Music is Art - Audio is Engineering

glucegen@excite.com (Radium) wrote in message news:<464c821f.0311091945.178c4a2d@posting.google.com>...
> Andrew Reilly <andrew@gurney.reilly.home> wrote in message news:<pan.2003.11.09.23.10.59.63234@gurney.reilly.home>...
> > On Sun, 09 Nov 2003 14:45:19 -0800, Radium wrote:
> > 
> > > What is the theoretically highest possible:
> > 
> > Based on what theory?  
> 
> Sampling rate = 2(highest frequency)

Fine, you just answered your own question.

> Bit resolution = dynamic range/2

Wrong. number of bits required to represent a dynamic range
of x dB is about x/6.02.

> bytes per second = information per time
> The high sample rate and bit resolution the better the audio quality.

Not so, you just stated so yourself. Once you have exceeded the
requirements for dynamic range and bandwidth, NO increease in
sampling rate or bits will give you any better resolution.

> The shortest amount of time is 10^-43 second. What is the maximum # of
> bits that can squeezed into this sml amt of time?

Are you REALLY serious or are you just a troll?

"Radium" <glucegen@excite.com> wrote in message
news:464c821f.0311091345.2c2c1f12@posting.google.com
> What is the theoretically highest possible:
>
> 1. Frequency Response (range of frequencies)

unlimited. You got the bits...

> 2. SNR

unlimited. You got the bits...

> 3. Dynamic Range

unlimited. You got the bits...

> 4. SPL

unlimited but irrlevant. You got the bits...

> 5. Musical Pitch (highest acceptable frequency)

unlimited

> of PCM audio?