Re: Radio waves...

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Bob S. wrote:
> I think you made an oops!  Check my math for oops:
>
> 56db = 20*Log_10(V2/V1)
>
> V2/V1 = 10^(56/20
>
> V2/V1 = 631 which fits easily into 9 bits.

It looks like I made an oops!   The old confusion of a factor of 10 with a
factor of 20 in front of the db log strikes again.  I naively took literally
what you wrote in a previous post:

> Those data rates don't seem to present a problem; Shannon says the  
> limiting bit rate is B*log_2(1+S/N)
> Taking a bandwidth B=3000 and a S/N level of 56 db (S/N=10^5.6=398107) 
>
> gives 3000*Log_2(398108) = 55808 bits/sec.
>  
> A good S/N ratio will get you there!

Here I just divided the 55808 by 3000 to get 18.6 bits = log_2(398108) =
log_2(1+10^(5.6)).  The dynamic range in bits comes from the log of the
S/N *amplitude* ratio, while the S/N level in db comes from the log of the
S/N *power* ratio.

> As regards the bandwidth of a standard telephone line,  I have seen 
> both the range (300-3300)Hz and the range (300-3400)Hz quoted in 
> the literature.  If crucial, I'll dig out a reference. Your figures 
> may represent an older standard.

You're probably correct here.  The number I used (2500 Hz) was from a fading
memory on the subject.  Your bandwidth figure here agrees with that given in
the web document you had referred to.  My original post on the subject was
an attempt to correct the faulty recollected audio bandwidth numbers posted
by Don about AM and FM broacasts by replacing them with my recollected
bandwidth numbers.  Apparently I had succumbed to the same thing (getting
caught posting from fading memory without checking) as Don, except in my
case the error here was in the telephone channel bandwidth.

It's good we have each other to fix each other's Mr. Know-it-all prima donna
posts.  Echoing what Leigh said earlier about how refreshing it is to have
the phys-l list members display a more questioning/skeptical feedback/
attitude than his latest crop of students -- I have to say that I agree --
such correction is good therapy.

David Bowman
dbowman@gtc.georgetown.ky.us