[CST-2] Info Theory

[Sam Staton]

Thanks -- my (stupid) mistake. When W is big (when trying to prove the
shannon limit), then the x in lg(1+x) is small, so the Taylor expansion is
sensible. However in this case the x is big, the Taylor cannot be so
truncated since the increasing terms are quite important.

-- 
sam



On Sun, 2 Jun 2002, Chris Applegate wrote:

> Yeah, that was my working too.
>
> A quick example of W=1, SNR = 99 (which can be thought of as a 0.01
> error rate, can't it?) gives 2.90 as the difference. The model answer
> does say 'about' when it says bandwidth, so presumably he has done some
> sort of approximation somewhere.
>
> Cheerio,
>
> Chris
> do something lastminute.work
>
> Chris Applegate
> Room X6, Corpus Christi College, Cambridge, CB2 1RH
> chris@qwghlm.co.uk / www.qwghlm.co.uk / [Redacted by SRCF sysadmins on request]
> ICQ 41706821          PGP key available on request
>
>
>
>
> > -----Original Message-----
> > From: cst-2-admin@srcf.ucam.org [mailto:cst-2-admin@srcf.ucam.org]On
> > Behalf Of Alvin
> > Sent: 2 June 2002 23:14
> > To: cst-2@srcf.ucam.org
> > Subject: Re: [CST-2] Info Theory
> >
> >
> > I think Daugman's working goes along the lines of:
> >
> > C = Wlog(1 + P/NW)
> >
> > C' = Wlog(1 + P/8NW)
> >
> >    ~= W(log(1 + P/NW) + log(1/8)
> >
> >     = W(log(1 + P/NW) - 3)
> >
> >     = C - 3W
> >
> > Which is a close approximation if P/NW was a lot larger than
> > 1...  What is
> > the norm for SNR anyway?
> >
> > Alvin
> >
> > > Just running through the info theory examples sheet again.
> > >
> > > Set 8, part d. I reckon C' = C/8 (approx) by the taylor
> > expansion of lg,
> > > (some brief experiments with gnuplot confirm this). Have I
> > misunderstood
> > > the question -- I read it as C' = W lg (1 + P/(8NW))
> > >
> > > ?
> > >
> > > Thanks
> >
> >
> >
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>
>
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