[John O'Flaherty]

On Mon, 22 Nov 2010 06:53:48 GMT, (Eric
Jacobsen) wrote:

On Sun, 21 Nov 2010 15:39:11 -0600, John O'Flaherty
wrote:

{trimmed}

Get a group of comm engineers in a room and see if anybody agrees on
the definition of SNR. Hint: don't get people started. There is no
single definition. deciBels are a similar animal. e.g., what is
power? What kind of power? RMS? Peak? Which is appropriate for
dB?

Power is rate of transfer of energy, and its time distribution, its
form, and its location of measurement require further specification,
but I don't see why dB shouldn't be applicable to all cases.

It is applicable, but it's not as clearly defined as some think or are
at least expressing here. Power measurement, as you just said,
requires integration over time. How much time? It is often
(usually) not specified, so there's already ambiguity in the
"definition" or "standard". "Instantaneous power" is a hand-wavy way
around that, but you can't measure that practically, so time
integration is required. How much is up to the implementer.

But the measurement procedure is a separate question from what power
is and what dB means.

{trimmed again}

Are there any actual examples of the use of dBFS that don't relate
to a full-scale voltage or current? Of course, the FS has to be
defined- voltage current, pressure. But I bet that anyone who was
using a full scale defined in terms of power would use a formula with
a factor of 10, not 20.

Actually, dBFS implies a digital number scale system, so the
traditional notions of voltage or current or power don't really even
apply any more. The analysis is performed on a numeric sequence,
which could represent anything. A single sample can be taken from
the numeric sequence, say X, and dBFS could be computed as either

ans = 10*log(X/FS) if one were interested in interpreting X as an
instantaneous power measurement (and ADCs often have internal
integration over some fraction of the sample period so that can be
argued). This follows the definition of RMS for a numeric sequence
when n = 1, as long as X is positive.

or

ans = 10*log(X/FS) if one were interested in interpreting X as a
voltage.

I'm assuming you meant 20 in that sentence. If so, I don't think we
disagree much. As you point out, when it's numeric, the use depends on
the interpretation. But if X _is_ being interpreted as a voltage, and
it is squared, then "ans" will be indistinguishable from a power
ratio.

I'd suggest, though, that one use whatever is consistent with the rest
of the analysis being performed.

There's nothing magical about the factor of 10 or 20. As always, one
just has to keep track of what one is doing and be consistent to get a
useful result.

Hard to argue with that!

{trimmed yet again}

Yes, dB per se is unitless but dBm and dBW aren't. +20 dB has no
units, but +20 dBm means 100 milliwatts. If you append RMS to dB,
that's a procedural specification, and you can have +10 dBVRMS, where
a unit is specified as well as the measurement procedure.
I agree that everything should be specified; nevertheless, if dB is
used for something that is not power, or not directly relatable to
power, I think it's being misused.

dBm and dBW are, actually, strictly speaking, still unitless or
dimensionless. The units cancel in the ratio of the reference and the
measurement, which HAVE to have the same units to get a meaningful
result. dBm and dBW (and others, but definitely not all) have the
odd property that they completely define a dimension, despite being
dimensionless. They still carry or reflect (or whatever) the
indicated dimensional unit with the quantity conveyed. Sort of.
IMHO, that's actually a hint that one has to pay attention to what one
is doing to get usable results.

Well, good point. You can't plug dBm into an ordinary equation and
have the units cancel correctly, so they just carry the information
about the unit.

--
John