Theoretically Highest Quality of PCM Audio

[Radium]

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?

 

[Dbowey]

what sampling rate do you have in mind?

 

[Andrew Reilly]

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.

 

[Les Cargill]

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".

 

[Dick Pierce]

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.

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

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.

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"

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.

 

[Radium]

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?

 

[Peter J. Kootsookos]

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.


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.

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.

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"


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

 

[Stewart Pinkerton]

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.

 

[Dick Pierce]

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?

 

[Arny Krueger]

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...

 

[Vladimir Vassilevsky]

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 is no theoretical limit.
However there are different standards which specify the performance, and
the different hardware limitations.

The today's state of art in the pro audio is ~24kHz, ~120dB, ~0.0005%
THD.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

 

[Jerry Avins]

unlimited. You got the bits...

Unlimited frequency response just by adding bits? Surely not to the word
length! One could argue that doubling the sample rate doubles the number
of bits, but it doesn't seem you meant that.

...

Jerry

 

[Maurice Givens]

If I am given a 16-bit fixed-point number of uniform quantization, I
can surely say that the maximum theoritic dynamic range I can get is
96.329 dB (assuming a voltage ratio and an constant impedance). If I
am told the sampling rate is a uniform 8 KHz, I can say that the
maximum unaliased frequency I can derive is theoritically, less than 4
KHz. Rather than say there is no therotical limit, let's just say we
don't have enough information to determine the limit.

Maurice Givens

 

[Vladimir Vassilevsky]

Nope. If you are given even a 1-bit quantization, you can have any
dynamic range by multiple oversampling. If the sample rate is 8 kHz, you
can have multiple channels combined into one stream of any bandwidth.
Vladimir Vassilevsky


DSP and Mixed Signal Design Consultant

http://www.abvolt.com

 

[Dbowey]

Vlad posted:

Nope. If you are given even a 1-bit quantization, you can have any
dynamic range by multiple oversampling. If the sample rate is 8 kHz, you
can have multiple channels combined into one stream of any bandwidth.
Vladimir Vassilevsky

So get real. That isn't what is being discussed.

 

[malcolm]

Nope. If you are given even a 1-bit quantization, you can have any
dynamic range by multiple oversampling. If the sample rate is 8 kHz, you
can have multiple channels combined into one stream of any bandwidth.
Vladimir Vassilevsky


DSP and Mixed Signal Design Consultant

http://www.abvolt.com

wont the noise start adding up as well and ruin the SNR !

 

[Andrew Reilly]

wont the noise start adding up as well and ruin the SNR !

Not if you declare your 8kHz system to have infinite (or at
least arbitrarily large) SNR (by making the number of bits per
sample arbitrarily large).

 

[Stewart Pinkerton]

wont the noise start adding up as well and ruin the SNR !

Not if you shape it so that most of it is outside the audio band.
That's how SACD works, and indeed it has very poor dynamic range above
20kHz.

 

[Arny Krueger]

Unlimited frequency response just by adding bits? Surely not to the
word length! One could argue that doubling the sample rate doubles
the number of bits, but it doesn't seem you meant that.

It's exactly what I meant.