What would be the fastest dial-up access speed if phone systems had 144 dB of dynamic range?

Hi:

The following is not a homework question. It is a question of my
curiosity.

Currently dial up internet access has a maximum theoretical speed of 64
kbps. This is due in part to the 48 dB dynamic range of telephone systems.

If telephones systems are updated so that they have a dynamic range of 144
dB instead of 48 dB, what will be the maximum theoretical speed of dial-up
internet access?


Thanks

"Green Xenon" <green_xenon1@yahoo.com> writes:

> Hi:
>
> The following is not a homework question. It is a question of my
> curiosity.
>
> Currently dial up internet access has a maximum theoretical speed of 64
> kbps. This is due in part to the 48 dB dynamic range of telephone systems.
>
> If telephones systems are updated so that they have a dynamic range of 144
> dB instead of 48 dB, what will be the maximum theoretical speed of dial-up
> internet access?

The easy answer is provided by the capacity formula

  C = W * log_2(1+P/N)
    = 4000 * 144/log_10(2)
    = 1.2 Mb/s
-- 
Randy Yates                      % "Midnight, on the water... 
Digital Signal Labs              %  I saw...  the ocean's daughter." 
mailto://yates@ieee.org          % 'Can't Get It Out Of My Head' 
http://www.digitalsignallabs.com % *El Dorado*, Electric Light Orchestra

Randy Yates <yates@ieee.org> writes:
> [...]

Doh! Just realized this is that weird dude. Sorry I responded!
-- 
Randy Yates                      % "Ticket to the moon, flight leaves here today 
Digital Signal Labs              %  from Satellite 2"
mailto://yates@ieee.org          % 'Ticket To The Moon' 
http://www.digitalsignallabs.com % *Time*, Electric Light Orchestra

On Mon, 16 Nov 2009 15:19:58 -0500, Randy Yates wrote:

> "Green Xenon" <green_xenon1@yahoo.com> writes:
> 
>> Hi:
>>
>> The following is not a homework question. It is a question of my
>> curiosity.
>>
>> Currently dial up internet access has a maximum theoretical speed of 64
>> kbps. This is due in part to the 48 dB dynamic range of telephone
>> systems.
>>
>> If telephones systems are updated so that they have a dynamic range of
>> 144 dB instead of 48 dB, what will be the maximum theoretical speed of
>> dial-up internet access?
> 
> The easy answer is provided by the capacity formula
> 
>   C = W * log_2(1+P/N)
>     = 4000 * 144/log_10(2)
>     = 1.2 Mb/s

... and is, unfortunately, wrong.

Without digging out my capacity formulae, 48dB is equivalent to 8 bits, 
and 144dB is equivalent to 24.  So assuming the original statement were 
correct you would triple the capacity, to 192kbps.

But that would only be if the capacity of dial up were actually 64kbps, 
which it isn't, or wasn't the last time I looked -- dial up maps to 8 
bits (not linearly), except that every once in a while the phone system 
'steals' the least significant bit for signaling.  You don't notice 
because they did such a good job with companding and such, but it is 
really missing, at a rate of something like 1/8 or 1/16th of the time.

So really fast dial-up modems are more like 56kbps, on a good day, _and_ 
they make that happen by figuring out how to hit the bit patterns of the 
D/A converter at the line card in the central office fairly exactly.

Not that you'd actually see 24 bits even if you increased the quality of 
the D/A converter -- 24 bits of precision is well below the threshold of 
seeing 2nd order effects, and into the really weird stuff.

-- 
www.wescottdesign.com

Tim Wescott <tim@seemywebsite.com> writes:

> On Mon, 16 Nov 2009 15:19:58 -0500, Randy Yates wrote:
>
>> "Green Xenon" <green_xenon1@yahoo.com> writes:
>> 
>>> Hi:
>>>
>>> The following is not a homework question. It is a question of my
>>> curiosity.
>>>
>>> Currently dial up internet access has a maximum theoretical speed of 64
>>> kbps. This is due in part to the 48 dB dynamic range of telephone
>>> systems.
>>>
>>> If telephones systems are updated so that they have a dynamic range of
>>> 144 dB instead of 48 dB, what will be the maximum theoretical speed of
>>> dial-up internet access?
>> 
>> The easy answer is provided by the capacity formula
>> 
>>   C = W * log_2(1+P/N)
>>     = 4000 * 144/log_10(2)
>>     = 1.2 Mb/s
>
> ... and is, unfortunately, wrong.

That's right, Tim. Arithmetic error!

  C = W * log_2(1+P/N)
    = 4000 * 14.4/log_10(2)
    = 191,343 b/s

> [...]

This other stuff is erudite drivel that basically depends on
assumptions. Seeing as how this guy is prone to wild questions, I see no
reason to laboriously debate assumptions when I've already honored the
question too much just providing a response.
-- 
Randy Yates                      % "I met someone who looks alot like you,
Digital Signal Labs              %             she does the things you do, 
mailto://yates@ieee.org          %                     but she is an IBM."
http://www.digitalsignallabs.com %        'Yours Truly, 2095', *Time*, ELO   

>"Green Xenon" <green_xenon1@yahoo.com> writes:
>
>> Hi:
>>
>> The following is not a homework question. It is a question of my
>> curiosity.
>>
>> Currently dial up internet access has a maximum theoretical speed of
64
>> kbps. This is due in part to the 48 dB dynamic range of telephone
systems.
>>
>> If telephones systems are updated so that they have a dynamic range of
144
>> dB instead of 48 dB, what will be the maximum theoretical speed of
dial-up
>> internet access?
>
>The easy answer is provided by the capacity formula
>
>  C = W * log_2(1+P/N)
>    = 4000 * 144/log_10(2)
>    = 1.2 Mb/s

What do "P" and "N" stand for?

>Not that you'd actually see 24 bits even if you increased the quality of 
>the D/A converter -- 24 bits of precision is well below the threshold of

>seeing 2nd order effects, and into the really weird stuff.


But isn't it possible to build phone systems than can handle 144 dB [24
bits] of dynamic range?

Also, what are the 2nd order effects?

I ask because I like the nostalgia of dial-up access but would like for it
to be faster than what it currently is.

As I write, I'm brainstorming about dial-up internet access in which all
the devices involved have a dynamic range of 144 dB and a bandwidth of 20
kHz [the same as human audio perception] as opposed to current dial-up
internet devices which have a bandwidth of only 4 kHz.

Green Xenon <green_xenon1@yahoo.com> wrote:
 
> The following is not a homework question. It is a question of my
> curiosity.
 
> Currently dial up internet access has a maximum theoretical speed of 64
> kbps. This is due in part to the 48 dB dynamic range of telephone systems.
 
> If telephones systems are updated so that they have a dynamic range of 144
> dB instead of 48 dB, what will be the maximum theoretical speed of dial-up
> internet access?

144dB sounds like more than the electronics, and especially the
electromechanical parts can do.  Do they also increase the sample rate?

The current phone system is mostly a digital 64kb/s system so obviously
the maximum rate is 64kb/s.

-- glen

>Green Xenon <green_xenon1@yahoo.com> wrote:
> 
>> The following is not a homework question. It is a question of my
>> curiosity.
> 
>> Currently dial up internet access has a maximum theoretical speed of
64
>> kbps. This is due in part to the 48 dB dynamic range of telephone
systems.
> 
>> If telephones systems are updated so that they have a dynamic range of
144
>> dB instead of 48 dB, what will be the maximum theoretical speed of
dial-up
>> internet access?
>
>144dB sounds like more than the electronics, and especially the
>electromechanical parts can do.  Do they also increase the sample rate?
>
>The current phone system is mostly a digital 64kb/s system so obviously
>the maximum rate is 64kb/s.
>
>-- glen
>

A dynamic range of 144 dB doesn't necessarily mean the equipment produces
signals that loud. 

Let's say the updated telephone systems have a dynamic range of 144 dB and
a bandwidth of 20 kHz [as opposed to 4 kHz]. What would be the maximum
speed possible of the dial-up internet access?

Green Xenon wrote:
>> Not that you'd actually see 24 bits even if you increased the quality of 
>> the D/A converter -- 24 bits of precision is well below the threshold of
> 
>> seeing 2nd order effects, and into the really weird stuff.
> 
> 
> But isn't it possible to build phone systems than can handle 144 dB [24
> bits] of dynamic range?

Yes. It is also possible to build phone systems with a 20KHz bandwidth. 
Who would pay for it?

> Also, what are the 2nd order effects?
> 
> I ask because I like the nostalgia of dial-up access but would like for it
> to be faster than what it currently is.
> 
> As I write, I'm brainstorming about dial-up internet access in which all
> the devices involved have a dynamic range of 144 dB and a bandwidth of 20
> kHz [the same as human audio perception] as opposed to current dial-up
> internet devices which have a bandwidth of only 4 kHz.

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