Linear PCM audio: 44.1 KHz, monaural, 1-bit-per-second

Andrew Reilly <andrew-newspost@areilly.bpc-users.org> writes:

> On Sun, 22 Jul 2007 23:52:26 -0400, Randy Yates wrote:
>
>> Andrew Reilly <andrew-newspost@areilly.bpc-users.org> writes:
>>> [...]
>>> I've only joined in to help those who want to emphasise that there
>>> is not necessarily any relationship between the sample rate or the
>>> quantization level of an audio system and the bit-rate of the
>>> encoded form.
>>
>> Show me a *linear PCM* system in which the bit-rate is not directly related
>> to the sample rate and sample width.
>
> How is that relevant?

Because the subject of this thread is "linear PCM" and the sample rate
and method of sampling are very pertinent to the definition of linear
PCM.

> By weaseling in with "sample width",

So to use the definition of "linear PCM" in a thread with "linear PCM"
in the subject line is to "weasel?" Curious opinion.

> you've already admitted the possiblity of scaling the bit rate
> independent of the sample rate.

No, I've not "admitted" it, I've insisted on it, if we are indeed speaking
of linear PCM.

> DSD is linear PCM, after all...

DSD is not linear PCM.

Linear PCM is defined in [proakiscomm] as follows:

Let x(t) denote a sample function emitted by a source and let x_n
denote the samples taken at a sampling rate f_s >= 2*W, where W is the
highest frequency in the spectrum of x(t). In PCM, each sample of the
signal is quantized to one of 2^R amplitude levels, where R is the
number of binary digits used to represent each sample. Thus the rate
from the source is R*f_s bits/s.

--Randy

@BOOK{proakiscomm,
title = "{Digital Communications}",
author = "John~G.~Proakis",
publisher = "McGraw-Hill",
edition = "fourth",
year = "2001"}

--
% Randy Yates % "Watching all the days go by...
%% Fuquay-Varina, NC % Who are you and who am I?"
%%% 919-577-9882 % 'Mission (A World Record)',
%%%% <yates@ieee.org> % *A New World Record*, ELO
http://home.earthlink.net/~yatescr

On Mon, 23 Jul 2007 06:59:44 -0400, Randy Yates wrote:

> Because the subject of this thread is "linear PCM" and the sample rate
> and method of sampling are very pertinent to the definition of linear
> PCM.

Subject, smubject. That's not what Radium was asking about.

>> DSD is linear PCM, after all...
>
> DSD is not linear PCM.

Sure it is. Two quantization levels, one bit per sample.

> Linear PCM is defined in [proakiscomm] as follows:
>
> Let x(t) denote a sample function emitted by a source and let x_n
> denote the samples taken at a sampling rate f_s >= 2*W, where W is the
> highest frequency in the spectrum of x(t). In PCM, each sample of the
> signal is quantized to one of 2^R amplitude levels, where R is the
> number of binary digits used to represent each sample. Thus the rate
> from the source is R*f_s bits/s.

And how is that different from DSD? f_s is >> 2*W, but that's not against
the rules.

Proakis is a fine work, and I agree with him, here. It's not gospel or
axiom, though.

--
Andrew

Andrew Reilly <andrew-newspost@areilly.bpc-users.org> writes:

> On Mon, 23 Jul 2007 06:59:44 -0400, Randy Yates wrote:
>
>> Because the subject of this thread is "linear PCM" and the sample rate
>> and method of sampling are very pertinent to the definition of linear
>> PCM.
>
> Subject, smubject. That's not what Radium was asking about.

In other words, forget what he wrote and begin discussing what you
think he means? No thanks. I'll stick with what's written.

>>> DSD is linear PCM, after all...
>>
>> DSD is not linear PCM.
>
> Sure it is. Two quantization levels, one bit per sample.

No, it's not. See below.

>> Linear PCM is defined in [proakiscomm] as follows:
>>
>> Let x(t) denote a sample function emitted by a source and let x_n
>> denote the samples taken at a sampling rate f_s >= 2*W, where W is the
>> highest frequency in the spectrum of x(t). In PCM, each sample of the
>> signal is quantized to one of 2^R amplitude levels, where R is the
>> number of binary digits used to represent each sample. Thus the rate
>> from the source is R*f_s bits/s.
>
> And how is that different from DSD? f_s is >> 2*W, but that's not against
> the rules.

It's not the sample rate that prevents DSD from being linear PCM, but the
fact that it does not utilize simple linear quantization.
--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

Radium wrote:

...

> To all:
>
> I have a neurological disability called Asperger's Syndrome.
>
> I would like to give you some information about my disability. The
> reason I am posting this message about Asperger's is to help avoid any
> potential misunderstandings [though it's probably too late].
>
> I have been diagnosed with Asperger's Syndrome (AS). AS is a
> neurological condition that causes significant impairment in social
> interactions. People with AS see the world differently and this can
> often bring them in conflict with conventional ways of thinking. They
> have difficulty in reading body language, and interpreting subtle
> cues. In my situation, I have significant difficulty with natural
> conversation, reading social cues, and maintaining eye contact. This
> can lead to a great deal of misunderstanding about my intent or my
> behavior. For example, I may not always know what to say in social
> situations, so I may look away or may not say anything. I also may not
> always respond quickly when asked direct questions, but if given time
> I am able express my ideas.
>
> On Usenet, the text-equivalent of my disability is probably noticed. I
> do apologize profusely, for any inconvenience it causes.
>
> Thank you very much in advance for your understanding, cooperation,
> and assistance.

Radium,

I declared my participation with this thread over, but this latest
revelation changes that. My grandson (who by coincidence arrives
tomorrow for a visit) has Asperger's too. He lived with me as my ward
during his difficult high-school years and a bit beyond, so I know about
the difficulties that the disability imposes at first hand. I also know
that it doesn't impair one's ability to reason about the physical world.

This Fall, my grandson enters his senior year of college. His grades are
generally good. Where he falls short is in the professorial ass-kissing
department, and I'm rather proud of that.

You can do (providing this Asperger's thing is real and not another
troll's ploy) whatever you want to do except, perhaps, make a good first
impression. You can take the trouble to learn what a bit really is and
discard the myth you have constructed about it. You can learn what a
binary number is and how to count in binary. You can learn that a sample
is a number that represents the measure of a signal at a particular
instant. When you have learned those things, come back and talk to us
about the DSP topics that interest you. If you want help learning those
things, come back sooner and ask for it. Until then, don't make yourself
seem more foolish than you are.

jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Andrew Reilly wrote:

> ... There isn't a relationship between bits/s and samples/s.




--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Jerry Avins wrote:
> Andrew Reilly wrote:
>
>> ... There isn't a relationship between bits/s and samples/s.

Please ignore previous message.

Jerry Avins wrote:

> Andrew Reilly wrote:
>
>> ... There isn't a relationship between bits/s and samples/s.

Just a reminder that some audio is more compressible than
others.

http://en.wikipedia.org/wiki/4%E2%80%B233%E2%80%B3

It seems that in this case, 4 minutes and 33 seconds of audio
can be compressed down to 3108 bytes as a zipped WAV file.

http://interglacial.com/~sburke/stuff/cage_433.html

91 bits/s, so a little more than the OP wanted.

-- glen

On Mon, 23 Jul 2007 10:35:03 -0400, Randy Yates wrote:

> It's not the sample rate that prevents DSD from being linear PCM, but the
> fact that it does not utilize simple linear quantization.

Yes, there's some fancy filtering up-stream, to ensure that the
quantization noise is non-white, but I'll maintain that what results is a
two-level/one-bit PCM signal, on the grounds that reconstruction to analog
involves reproducing the corresponding sequence of impulses or levels and
low-pass filtering it.

Of course, exactly the same techniques are also used in the
quantization of multi-bit PCM, these days, for much the same effect.

--
Andrew

Andrew Reilly <andrew-newspost@areilly.bpc-users.org> writes:

> On Mon, 23 Jul 2007 10:35:03 -0400, Randy Yates wrote:
>
>> It's not the sample rate that prevents DSD from being linear PCM, but the
>> fact that it does not utilize simple linear quantization.
>
> Yes, there's some fancy filtering up-stream, to ensure that the
> quantization noise is non-white, but I'll maintain that what results is a
> two-level/one-bit PCM signal, on the grounds that reconstruction to analog
> involves reproducing the corresponding sequence of impulses or levels and
> low-pass filtering it.
>
> Of course, exactly the same techniques are also used in the
> quantization of multi-bit PCM, these days, for much the same effect.

Andrew: Get over it. You're wrong on this issue.

A DSD quantizer has memory. A linear quantizer does not. DSD != PCM.
--
% Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven.
%% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and
%%% 919-577-9882 % Verdi's always creepin' from her room."
%%%% <yates@ieee.org> % "Rockaria", *A New World Record*, ELO
http://home.earthlink.net/~yatescr

On Mon, 23 Jul 2007 18:39:10 -0400, Randy Yates wrote:

> A DSD quantizer has memory. A linear quantizer does not. DSD != PCM.

Any quantizer that frequency-shapes the quantization noise has state, just
like any other filter, and such quantizers exist (and are in widespread
use) in multi-bit PCM systems. White quantization noise isn't the
definition of PCM, and I'm surprised that you would suggest that it was.

--
Andrew