[John O'Flaherty]

On Sun, 21 Nov 2010 05:23:37 GMT, (Eric
Jacobsen) wrote:

On Sat, 20 Nov 2010 17:19:53 -0600, John O'Flaherty
wrote:

On Sat, 20 Nov 2010 20:44:55 GMT, (Eric
Jacobsen) wrote:

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.

But it isn't an independent way of rescaling a measurement. If it
were, then the formula for dB as a ratio of voltages would have the
same form as that for a ratio of powers: 10 * log(v2/v1). The fact
that it has 20 means that it is squaring the voltage ratio to make it
a power ratio (implicitly assuming constant impedance). It's a hybrid
system of units when it is dBV, but it still represents a power ratio.
Wikipedia offers this definition for "decibel":
"A ratio in decibels is ten times the logarithm to base 10 of the
ratio of two power quantities.", citing this:
" IEEE Standard 100 Dictionary of IEEE Standards Terms, Seventh
Edition, The Institute of Electrical and Electronics Engineering, New
York, 2000; ISBN 0-7381-2601-2; page 288"

This isn't to say that it's not used otherwise, but that's the
definition.

The issue is that it's muddy and not consistently used and hasn't been
nearly since inception. Antenna gains, e.g., dBi, Sound pressures,
e.g., dBSPL, radar cross sectional area, dBsm, bandwidth, e.g., dBHz,
and the current topic, dBFS, are often used with or implemented with
power measurements, but they aren't really power, and sometimes don't
have anything to do with power.

But antenna gains are compared to the power provided by an isotropic
antenna, aren't they? For dBSPL, it's a power measurement too. Though
it's called a pressure level, the defining formula involves pressure
squared, so it should be interpreted as the pressure corresponding to
a particular power level. What criterion do you use to decide whether
to include a factor of 10 or a factor of 20 in your formula?

The point is that it's just an equation to plug numbers into, and the
meaning is only relevant to the interpretation of what got plugged in.

Things like dBFS, or even dBC or other common applications of
deciBels, are very often ambiguous and have to have additional context
or explanation if one really wants to remove all ambiguity.

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.

There are common uses that usually apply, but there are enough
inconsistencies that one has to be very careful. When writing, if in
doubt, spell it out. When reading, if in doubt, don't assume
anything, because it could be anything.

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.

Why then is a factor of 20 used for voltages rather than a factor of
10? 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.

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.

It's true that the input units must be the same, but dB is actually
unitless, since it's a ratio of two like units.
Again, from Wikipedia:
"Being a ratio of two measurements of a physical quantity in the same
units, it is a dimensionless unit."

It is a dimensionless unit, but it can preserve the dimensions of the
input value. Or reflect them, whatever you want to call it.
Provide any quantity in dBm, or dBW, and without any other information
you also know the power level dimensions without ambiguity. That's
an odd thing to be able to do with a dimensionless number or a
dimensionles unit, whatever you wish to call it.

So one has to keep track of what's going on, regardless of what
Wikipedia says. Experienced people still get tripped up on it all
the time.

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.


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.

--
John