Determining the Maximum Power Through a Band-Limited, Fixed-Point Signal Path

On Jun 28, 1:25 pm, Jerry Avins <j...@ieee.org> wrote:
> dbd wrote:
>    ...
> > A constant value of 1.0 or -1.0 would put through the maximum
> > power and be band limited to a tiny fraction of the Nyquist frequency.
>
> Not zero mean, though. You need to switch once in a while.
>    ...
> Jerry
> --


'zero mean' was not a part of the original problem description.
It was an assumption the OP made about his first guess at a
solution, for the purpose of justifying a calculation of variance.

The OP then stated: "This doesn't make me happy..."

That's why I asked if the OP wanted to extent the problem description.

Dale B. Dalrymple
http://dbdimages.com

dbd wrote:

   ...

> 'zero mean' was not a part of the original problem description.
> It was an assumption the OP made about his first guess at a
> solution, for the purpose of justifying a calculation of variance.
> 
> The OP then stated: "This doesn't make me happy..."
> 
> That's why I asked if the OP wanted to extent the problem description.

You were right all along. Randy probably has a clearer picture now. (We 
can ask him when he comes out from under the rock. :-)  )

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

Jerry Avins <jya@ieee.org> writes:

> dbd wrote:
>
>   ...
>
>> 'zero mean' was not a part of the original problem description.
>> It was an assumption the OP made about his first guess at a
>> solution, for the purpose of justifying a calculation of variance.
>> The OP then stated: "This doesn't make me happy..."
>> That's why I asked if the OP wanted to extent the problem
>> description.
>
> You were right all along. Randy probably has a clearer picture
> now. (We can ask him when he comes out from under the rock. :-)  )

Well, I did say to assume a zero-mean random signal, but that was only
in my random signal solution. The problem was originally stated as
"bandlimited," which by common usage includes DC, so Dale's solution 
is valid by that definition.

Am I growing senile, or has the term "bandlimited" changed meaning over
the last couple of decades or so? Why would common usage take it to mean
"zero above some frequency" when "lowpass" means precisely that? It 
seems like the term would have more utility if it were allowed to mean
something more general.

And actually, I found an IEEE reference [tyler] (albeit a couple of decades old)
in which the term is used to mean something more general. 

--Randy


@article{tyler,
  title = "{A Companding System for Multichannel TV Sound}",
  author = "Leslie B. Tyler and Mark F. Davis and William A. Allen",
  journal = "IEEE Transactions on Consumer Electronics",
  month = "November",
  year = "1984"}

-- 
%  Randy Yates                  % "How's life on earth? 
%% Fuquay-Varina, NC            %  ... What is it worth?" 
%%% 919-577-9882                % 'Mission (A World Record)', 
%%%% <yates@ieee.org>           % *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Randy,

Come on back on top of the rock in the sun with
the rest of us. You can't keep all the ELO to
yourself down there.

Dale B. Dalrymple
http://dbdimages.com

Randy Yates wrote:

   ...

> Am I growing senile, or has the term "bandlimited" changed meaning over
> the last couple of decades or so? Why would common usage take it to mean
> "zero above some frequency" when "lowpass" means precisely that? It 
> seems like the term would have more utility if it were allowed to mean
> something more general.

I think you're dead on about the "ought" part. What we see here is a 
general debasement of the language that goes on all the time. 
"Bandwidth" has an entirely new (and fallacious) meaning nowadays, too. 
I've given up trying to get people to distinguish bit rate from baud 
rate, and even bothering to distinguish them myself in speech. I think 
it's a case of "Read it and weep."

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

Randy Yates wrote:
(snip)

> I'm not sure where the misunderstanding is. I stated that I wanted
> to know the maximum power through a bandlimited, fixed-point signal path.
> That, in general, does not include DC. 

In most cases, band limited means a maximum frequency with
0 Hz being the lower limit.  (Well, if you include negative
frequencies, +/- the band limit.)

I agree that it doesn't have to be that way, but if you don't
want to include DC, you should state that in the beginning.

-- glen

Randy Yates wrote:

(snip)

> For example, let's say I have a 16-bit two's complement signal path,
> and it's band-limited to 1/4 of Nyquist. What is the maximum signal
> power I can transmit through such a path? 

Not so long ago the question of the highest amplitude sine that
could be digitized within a +/- 1 system.  One possibility is
at Nyquist/2, with samples +1, +1, -1, -1, repeating, which
is a sine with amplitude sqrt(2).

For any sine frequency with a period that is an integer number
of samples you can find the largest amplitude that you can fit
in between sample points.  For Nyquist/N, and period 2N I believe
it is amplitude sec(pi/(2N)), N>1.

-- glen