On Sat, 20 Nov 2010 15:09:19 -0500, Randy Yates
wrote:
John O'Flaherty writes:
On Fri, 19 Nov 2010 21:46:25 -0500, Randy Yates
wrote:
(Scott Dorsey) writes:
In article , Randy Yates wrote:
If dBFS is defined as
dBFS = 20 * log_10(XRMS / (RMS value of full-scale sine wave),
where XRMS is the RMS value of the digital data stream, and you're
generating a "digital square wave," then you are wrong. The digital
square wave can go to +3dBFS as defined above.
dBFS has not got a damn thing to do with sine waves or reference levels
or anything in the analogue world.
Again, I'm not asking how it's not defined, I'm asking how it is
defined.
You guys have danced around this one all day. It's getting humorous.
It has ONLY to do with how far a digital level is below the point at
which the digital value reaches full scale (all bits on).
If you know what it means, and you're literate, then you should be able
to come up with a precise definition. I haven't seen one yet.
The problem is that dB is defined as a unit of power, usually applied
to signals with some time duration.
YES!!! Thank you, John!
Except he's wrong.
As others have said, dB is a way of rescaling and is independent of
the units involved or the characteristics of the measurement. It is
simply the scaled log of a ratio, where one of the terms in the ratio
is a reference level. If the reference level and the measurement
have units of power, then the resulting dB value will have units of
power, and will usually reflect that, e.g., dBm, dBW, etc. If the
reference level and measurement have units of amplitude, then the
output will generally reflect that as well, e.g., dBV.
Perhaps the confusion is that FS is unitless and can be anything;
power, amplitude, time, price, whatever. Since it is just a
reference to a number within a number system, the output will then
have the units of whatever that number represents. Meanwhile, since
it is just a number within a particular dynamic range indicated by FS,
dBFS is still a useful expression for evaluating a system.
But it is not inherently power or amplitude or anything. It takes on
the units (or unitlessness) of whatever the number system represents.
Obviously, a square wave at full scale of a converter has more power
than, say, a sine wave or a 1% duty cycle signal at full scale. So,
how can one define dBFS so it represents how the figure is actually
used?
Not a bad question, but I was hoping there was _THE_ definition.
Apparently there is not. And this is really the crux of the issue (for
dBFS). Some people say it's a peak (instantaneous) measurement, yet I
see meters that use it for RMS measurements. I'm afraid the truth is
that there is no universal meaning for it like there is for dBm, dBV,
and several other dB units.
dBx always takes on the units of the input values. The reference and
the measurement have to have the same units for the result to be
meaningful.
How about "a signal at 0 dBFS is one whose instantaneous power
I'm not comfortable with the concept of "instantaneous power." Rather, I
think we have to just concede that the "dB" sometimes breaks tradition
and works with instantanous quantities rather than power.
It can be anything. Instantaneous, averaged, glacial, whatever.
Time may not be involved at all, or it might be.
reaches but never exceeds the instantaneous power associated with full
scale of the converter"? Modifying your formula above, dBFS = 20 *
log_10(peak signal voltage / converter maximum voltage)
That is essentially what I wrote last night. Thanks for your input, John.
--
Randy Yates % "Maybe one day I'll feel her cold embrace,
Digital Signal Labs % and kiss her interface,
% til then, I'll leave her alone."
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com