[Elecraft] Digital, Smigital...

[Ron D'Eau Claire]

But isn't conventional SSB as used on the Ham bands transmitted in analog
form, regardless of how the signal was created and so limited like any other
analog signal constricted to the same bandwidth?

Ron AC7AC

-----Original Message-----

On Oct 4, 2010, at 12:41 PM, John Ragle wrote:

>  I must be missing something here. How can one expect high fidelity audio 
> (e.g. 20 HZ to 20 kHz) with a receiver with a pass-band of 2.5 or 3.0 
> kHz?
> 
> With those strictures, one is always going to get "carbon mike" or 
> slightly better audio, no?

No.

The data rate through a channel depends not just on the analog bandwidth of
a channel, but also the SNR of the channel.

See the section "The Capacity of a Continuous Channel" in Part IV
(Continuous Channel) in Shannon's 1948 BSTJ paper:

http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf

Channel capacity in bits/sec is equal to W, the bandwidth, multiplied by the
log(base 2) of the (S+N)/N ratio.  

With appropriate modulation and error correction coding, [Shannon shows
that] you can transmit a digital signal, with *any* arbitrarily small,
non-zero error bound that you wish to set, at a data rate up to the channel
capacity.

E.g., 

Consider a 3 kHz wide channel with (S+N) to N ratio of 30 dB.  The power
ratio is 1000, thus log2 is 9.96 [2 to the power of 10 = 1024, so log2(1000)
is just under 10].  With appropriate modulation and coding, from Shannon,
you can potentially get almost 30 kbits/sec of digital data through such a
channel.

A practical modem from the 1980s can do 28.8 and 33.6 kbits/second through a
3 kHz telephone circuit.  The 56 kbits/sec modems achieve the higher rate by
using source coding in addition to channel coding, but they cannot maintain
56 kb/s with completely random binary data.

Today's DSL modems can do even better (much better), but they depend on the
landline's capability to send, albeit attenuated, signals beyond the 3 kHz
voice band.

Off Topic:

You can perhaps understand why some of us revere Claude Shannon much more
than we do Albert Einstein :-).

http://en.wikipedia.org/wiki/Claude_Shannon

The above Wiki article also refers to Shannon's Master's thesis which
connected relay circuits with Boolean Algebra -- making it possible to talk
about AND gates and OR gates.  David Huffman, also in a Master's thesis,
added the memory element (what we call flip-flops today).  The combination
is what makes it possible for me to type this and for you to read it :-).

73
Chen, W7AY