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

On Jul 21, 9:19 pm, Jerry Avins <j...@ieee.org> wrote:
> glen herrmannsfeldt wrote:
> > Jerry Avins wrote:
> > (snip)
>
> >> Bits don't come in fractional parts.
>
> > a little out of context, but mostly I don't agree.
>
> > A decimal digit is worth about 3.32 bits. In any
> > digital system where the number of possible levels
> > isn't a power of two you have fractional bits.
>
> A decimal digit may be *worth* about 3.32 binary bits, but because bits
> don't come in fractional parts, *representing* a decimal digit requires
> rounding up to 4.

Only in binary. In a ten voltage-levels system, you
would not need to round up in the representation.
The possible information content could be more than
3 bits worth, but trying to put 4 bits worth of data
down the channel might result in information loss.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

jim wrote:
>
> Jerry Avins wrote:

...

>> I wasn't clear. Each transaction if paid for when it happens: no credit.
>> What coin is used for the payments?
>>
>
> I don't see the relevance of that question to the original problem.
> There is nothing I saw that indicated he wanted to determine the value
> of the 1 bit per second before each second had elapsed.

I wasn't addressing that part of the thread. He wants to represent
44,100 *uncompressed* sample with a single bit. He seems to feel that
each sample can be represented by 1/44,100th of a bit. My analogy was
intended to indicate that some things are indivisible.

As a measure of information, fractions of a bit make sense. Fractal
geometry makes sense too. Nevertheless, there are applications where
buts and dimensions must be counted with integers.

> Actually this thread caught my eye because there seems to be some sort
> of inverse law of silliness operating here. If the OP had asked can he
> take 41KHz 16 bit PCM and convert it to 8kHz 8bit he would have gotten
> some pretty serious answers. If he had asked could he convert to 2kHz
> with 4 bits the answers would have been a bit less sober. It appears
> that if the sample and bit rate of the question drops low enough the
> answers appear to approach lunacy. That's a very interesting tidbit of
> DSP trivia I wasn't aware of.

This is the third incarnation of Radium's delusion. You already missed
two opportunities to notice!

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

Ron N. wrote:
> On Jul 21, 9:19 pm, Jerry Avins <j...@ieee.org> wrote:
>> glen herrmannsfeldt wrote:
>>> Jerry Avins wrote:
>>> (snip)
>>>> Bits don't come in fractional parts.
>>> a little out of context, but mostly I don't agree.
>>> A decimal digit is worth about 3.32 bits. In any
>>> digital system where the number of possible levels
>>> isn't a power of two you have fractional bits.
>> A decimal digit may be *worth* about 3.32 binary bits, but because bits
>> don't come in fractional parts, *representing* a decimal digit requires
>> rounding up to 4.
>
> Only in binary. In a ten voltage-levels system, you
> would not need to round up in the representation.
> The possible information content could be more than
> 3 bits worth, but trying to put 4 bits worth of data
> down the channel might result in information loss.

Only in binary do you have bits. In base three, you have trits, and so
forth. When something is measured by counting bits, base two is implied.
That is not to say that the equivalence to another measure can't involve
fractional bits, but when the representation is binary, there are are no
fractional bits. It's another story with brick; there one can have bats,
queen closers, king closers, and other fractional sizes. But bricklayers
have brick chisels. I don't believe there's a way to split a digit in
any base; it's either there or it's not. (Preemptive strike: A 3 1/2
digit mater is a code name, not an accurate description.)

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

glen herrmannsfeldt wrote:
>
> jim wrote:
> (snip)
>
> > Actually this thread caught my eye because there seems to be some sort
> > of inverse law of silliness operating here. If the OP had asked can he
> > take 41KHz 16 bit PCM and convert it to 8kHz 8bit he would have gotten
> > some pretty serious answers. If he had asked could he convert to 2kHz
> > with 4 bits the answers would have been a bit less sober. It appears
> > that if the sample and bit rate of the question drops low enough the
> > answers appear to approach lunacy. That's a very interesting tidbit of
> > DSP trivia I wasn't aware of.
>
> I presume there is a point at which it can't be called audio anymore.

Bits or digital data can never be called audio. You need some sort of
mechanism to make it into something audible. You could certainly invent
a mechanism that would convert this to sound. I don't know why one would
do this and I don't think anybody would be using the words "perfect
reconstruction" whilst doing it but it could be done.

-jim





>
> I don't really know where that point is, but it seems likely more than
> one bit/second. It does depend on what you allow for input, though.
> Say, for example, that the input audio was silent for a large fraction
> of the time. A good compression method should be able to take that into
> consideration and not store (many) bits for the silent part. In that
> case, there may be more than enough bits left for the non-silent part.
>
> What is the average number of bits/second needed to reproduce the
> audio in a concert hall averaged over its life? Most of the time
> it is empty and quiet, though sometimes there might be a noisy
> vacuum cleaner and other times a symphony practice session.
> I could imagine 90% of the time as quiet, though.
>
> -- glen

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jim wrote:
(snip)

> Actually this thread caught my eye because there seems to be some sort
> of inverse law of silliness operating here. If the OP had asked can he
> take 41KHz 16 bit PCM and convert it to 8kHz 8bit he would have gotten
> some pretty serious answers. If he had asked could he convert to 2kHz
> with 4 bits the answers would have been a bit less sober. It appears
> that if the sample and bit rate of the question drops low enough the
> answers appear to approach lunacy. That's a very interesting tidbit of
> DSP trivia I wasn't aware of.

I presume there is a point at which it can't be called audio anymore.

I don't really know where that point is, but it seems likely more than
one bit/second. It does depend on what you allow for input, though.
Say, for example, that the input audio was silent for a large fraction
of the time. A good compression method should be able to take that into
consideration and not store (many) bits for the silent part. In that
case, there may be more than enough bits left for the non-silent part.

What is the average number of bits/second needed to reproduce the
audio in a concert hall averaged over its life? Most of the time
it is empty and quiet, though sometimes there might be a noisy
vacuum cleaner and other times a symphony practice session.
I could imagine 90% of the time as quiet, though.

-- glen

Jerry Avins wrote:

(snip)

> I wasn't addressing that part of the thread. He wants to represent
> 44,100 *uncompressed* sample with a single bit. He seems to feel that
> each sample can be represented by 1/44,100th of a bit. My analogy was
> intended to indicate that some things are indivisible.

I read it as an average rate of 1 bit/second, after some compression
method. I make no suggestion on what compression method might
be able to do that.

-- glen

Jerry Avins wrote:
(snip)

> We're not tuned into the same station. Bits are binary digits, just as
> the roman numerals we use are decimal digits. I claim that one decimal
> digit or four bits can represent one particular level out of ten. Do you
> think I miss a point? If so, what point?

Three decimal digits can be stored in 10 bits.

http://publibfi.boulder.ibm.com/epubs/pdf/a2322320.pdf

I might have been happy with BCD but it seems that IBM wasn't.
This is a pretty amazing format, not yet standardized by IEEE,
but maybe not much longer. It not only holds three digits in
10 bits, but also splits bits between the significand and
exponent. That is, five bits can hold one decimal digit
and one trinary trit, extending the exponent range.

As for your other example, a 3.5 digit DVM should allow up
to two for the MSD, that is, up to 2.999.

10**(0.5) is close to 3, 10**(0.3) is close to 2, so for
most DVMs 3.3 or 4.3 digits would be more accurate.

-- glen

-- glen

Radium wrote:
> what would such audio sound like? Bad-quality?

tic tac tic tac .....

>
>
> Thanks,
>
> Radium
>

glen herrmannsfeldt wrote:
> Jerry Avins wrote:
>
> (snip)
>
>> I wasn't addressing that part of the thread. He wants to represent
>> 44,100 *uncompressed* sample with a single bit. He seems to feel that
>> each sample can be represented by 1/44,100th of a bit. My analogy was
>> intended to indicate that some things are indivisible.
>
> I read it as an average rate of 1 bit/second, after some compression
> method. I make no suggestion on what compression method might
> be able to do that.

Did you read Radium's kick-off post? I'll repeat it here.

###############################

Hi:

Is the following possible?:

A linear uncompressed PCM audio file whose sample-rate is 44.1 KHz,
monaural, and with a bit-rate of 1-bit-per-second.

The 1-bit-per-second is because the bit-resolution [normally 16-bit in
CD audio] is only 1-bit-per-44,100 samples in this hypothetical case.
Since the sample-rate is 44.1 KHz, and there is only 1 channel [due to
the monaural audio], the bit-rate is 1-bit-per-second.

Bit rate = sample rate X bit-resolution X # of channels

44,100 Hz X 1/44,100-bit X 1 channel = 1

Please note that the 1/44,100-bit is not a fractional bit-resolution
but rather it represents the fact that there is only 1 bit for every
44,100 samples.

Is the above scenario possible? Did I explain it correctly? If so,
what would such audio sound like? Bad-quality?


Thanks,

Radium

###############################

I repeat, uncompressed and only one bit for every 44,100 samples.

To reiterate,
He doesn't know what a bit is.
He doesn't know what a sample is.

Since we have gone over this same ground before, he is either a talented
troll or hopelessly mired in his misconceptions.

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

On Jul 22, 12:37 pm, glen herrmannsfeldt <g...@ugcs.caltech.edu>
wrote:

> I read it as an average rate of 1 bit/second, after some compression
> method. I make no suggestion on what compression method might
> be able to do that.

Any help here? Is there any type of compression that most closely
resembles linear-PCM and can do the task of less than 1-bit-per-cycle?

One-bit-per-44,100-cycles is what I was originally looking for.
However, as some posters have stated, all I would hear in 1-bit-per-
cycle would resemble a square wave "tick tock".

So how about decreasing the amount of bits-per-cycle so that the bit-
rate becomes 20,000-bits-per-second? After all the human auditory
system perceives up to 20 KHz so covering the entire human audio
frequency range would require at least 20-kilobits-per-second.

In a sample rate of 44,100-cycles-per-second, this would best be done
at 1-bit-every-2-cycles. This would give a bit-rate of 22,050-bits-per-
second. That's obviously above 20kbits-per-second but only slightly.