FPGA Central

Hi,
this question might be very trivial, but I haven't found good explanatio
anywhere else.

I have an audio signal - some sine. Use a wavelabl to look at th
waveform, and its maximum is at about 0.6. When I change the display int
dB it shows about -5dB at that level.
But this does not make sense - the formula is 10*log10(amplitude). So i
should be -2.5dB. I have found, that this is because we use squares fo
comparison :
10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)

They say it is often used in electronics to compare voltages, but why i
it used in digital audio? Yeah I know that the digital values ar
equivalent to resulting electrical power, but we are not comparing anythin
to anything. So why should we square?

And if so, then when should we NOT square?

Thanks a lot.
dmnc

On Oct 7, 2:52*pm, "jungledmnc" <jungled...@gmail.com> wrote:
> Hi,
> this question might be very trivial, but I haven't found good explanation
> anywhere else.
>
> I have an audio signal - some sine. Use a wavelabl to look at the
> waveform, and its maximum is at about 0.6. When I change the display into
> dB it shows about -5dB at that level.
> But this does not make sense - the formula is 10*log10(amplitude). So it
> should be -2.5dB. I have found, that this is because we use squares for
> comparison :
> 10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)
>
> They say it is often used in electronics to compare voltages, but why is
> it used in digital audio? Yeah I know that the digital values are
> equivalent to resulting electrical power, but we are not comparing anything
> to anything. So why should we square?
>
> And if so, then when should we NOT square?
>
> Thanks a lot.
> dmnc


Hello dmnc,


dB = 10*log(power/power_reference)

now since power is proportional to amplitude squared then

dB = 20*log(amplitude/amplitude_reference)

With dB we are really always talking about power relative to a
reference power.

Even in acoustics, we have 100 dB is 0.946 watts per square meter.

I hope this helps.

Clay

jungledmnc wrote:
> Hi,
> this question might be very trivial, but I haven't found good
> explanation anywhere else.
>
> I have an audio signal - some sine. Use a wavelabl to look at the
> waveform, and its maximum is at about 0.6. When I change the display
> into dB it shows about -5dB at that level.
> But this does not make sense - the formula is 10*log10(amplitude). So
> it should be -2.5dB. I have found, that this is because we use
> squares for comparison :
> 10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)
>
> They say it is often used in electronics to compare voltages, but why
> is it used in digital audio? Yeah I know that the digital values are
> equivalent to resulting electrical power, but we are not comparing
> anything to anything. So why should we square?
>
> And if so, then when should we NOT square?
>
> Thanks a lot.
> dmnc

I checked your numbers. You need to pay close attention to what is being
compared when you talk about dB. Because, dB is always a comparison of
amplitudes.

You say "its maximum is about 0.6" but don't give any dimensions like
"volts" for example.
Then, you don't give the reference which is usually 1 volt.... but that is
*usually* understood to mean 1vrms. So, 1vrms would be 0dB.

From 20log(0.6) I get -4.4dB ... which really means
20log(0.6) - 20log(1.0) so the dimensions are likely mixed:
Peak voltage for the 0.6 and rms voltage for the 1.0.

Converting 0.6v peak to rms is 0.6 x 0.707 = 0.42 vrms
20log(0.42) = -7.4dB

So, I'm not sure where you are on all this with your wavelab1.

[email protected] in *ERRROOOORRRR* wrote:

>
> Even in acoustics, we have 100 dB is 0.946 watts per square meter.
>

I would agree IF *and only* IF you stated dbV, dbm, or db.... with
stated/implied load/impedance/****

Signed: local (not so quite) nit picker

glen herrmannsfeldt <[email protected]> writes:

> Richard Owlett wrote:
>
>> [email protected] in *ERRROOOORRRR* wrote:
>
>>> Even in acoustics, we have 100 dB is 0.946 watts per square meter.
>
>> I would agree IF *and only* IF you stated dbV, dbm, or db.... with
>> stated/implied load/impedance/****
>
> I presume that is for a propagating wave in air. The actual power
> that goes into some detector (or other medium) depends on the
> impedance in that medium.

But it's just like the electrical situation - if we assume the
same impedance for the reference as for the measured signal,
the two cancel and don't really matter - we can compute it from
the amplitudes (or equivalently, sound intensities).

I think Richard is right. I think what Clay meant was 100 dB SPL.
--
% Randy Yates % "Watching all the days go by...
%% Fuquay-Varina, NC % Who are you and who am I?"
%%% 919-577-9882 % 'Mission (A World Record)',
%%%% <[email protected]> % *A New World Record*, ELO
http://www.digitalsignallabs.com

Richard Owlett wrote:

> [email protected] in *ERRROOOORRRR* wrote:

>> Even in acoustics, we have 100 dB is 0.946 watts per square meter.

> I would agree IF *and only* IF you stated dbV, dbm, or db.... with
> stated/implied load/impedance/****

I presume that is for a propagating wave in air. The actual power
that goes into some detector (or other medium) depends on the
impedance in that medium.

For an EM wave in a wire, you need the impedance, in air you don't.

-- glen

On Oct 7, 2:52*pm, "jungledmnc" <jungled...@gmail.com> wrote:
> Hi,
> this question might be very trivial, but I haven't found good explanation
> anywhere else.
>
> I have an audio signal - some sine. Use a wavelabl to look at the
> waveform, and its maximum is at about 0.6. When I change the display into
> dB it shows about -5dB at that level.
> But this does not make sense - the formula is 10*log10(amplitude). So it
> should be -2.5dB. I have found, that this is because we use squares for
> comparison :
> 10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)
>
> They say it is often used in electronics to compare voltages, but why is
> it used in digital audio? Yeah I know that the digital values are
> equivalent to resulting electrical power, but we are not comparing anything
> to anything. So why should we square?
>
> And if so, then when should we NOT square?
>
> Thanks a lot.
> dmnc

dB's always compare one power to another power by the formula that you
have written down.

In electronics we often do not directly measure power, but rather
voltage. Most of our measuring equipment measures things in voltage.

So we are stuck in a position where we want to compare one power level
to another power level, but our measuring equipment measures voltages.

(Also in DSP most of the time the A/D converter is getting a voltage
equivelent input)

To properly compare one power level when we made the measurement in
voltage you have to first convert the measured voltage level into a
measured power level, and the reference voltage level into a reference
power level.

Here is where the shortcut comes in, but remember, dB's always compare
power levels. It is the definition.

But when you are comparing voltage levels, it turns out you get to use
the trick of multiplying by 20*log(ratio) instead of 10*log(ratio),
becuase power proportional to the voltage squared. so 10*log(V1^2/
V2^2) is the same as

20*log(V1/V2). This is a shortcut or trick. Always go back to dB's
compare power per the definition formula 10*log(P1/P2).

The 20 log thing comes into play becuase in the real world you rarely
measure power directly. You measure voltages directly, and then
apply the 20* trick to convert the voltages to power.

On Oct 7, 11:07*pm, buleg...@columbus.rr.com wrote:
> On Oct 7, 2:52*pm, "jungledmnc" <jungled...@gmail.com> wrote:
>
>
>
>
>
> > Hi,
> > this question might be very trivial, but I haven't found good explanation
> > anywhere else.
>
> > I have an audio signal - some sine. Use a wavelabl to look at the
> > waveform, and its maximum is at about 0.6. When I change the display into
> > dB it shows about -5dB at that level.
> > But this does not make sense - the formula is 10*log10(amplitude). So it
> > should be -2.5dB. I have found, that this is because we use squares for
> > comparison :
> > 10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)
>
> > They say it is often used in electronics to compare voltages, but why is
> > it used in digital audio? Yeah I know that the digital values are
> > equivalent to resulting electrical power, but we are not comparing anything
> > to anything. So why should we square?
>
> > And if so, then when should we NOT square?
>
> > Thanks a lot.
> > dmnc
>
> dB's always compare one power to another power by the formula that you
> have written down.
>
> In electronics we often do not directly measure power, but rather
> voltage. *Most of our measuring equipment measures things in voltage.
>
> So we are stuck in a position where we want to compare one power level
> to another power level, but our measuring equipment measures voltages.
>
> (Also in DSP most of the time the A/D converter is getting a voltage
> equivelent input)
>
> To properly compare one power level when we made the measurement in
> voltage you have to first convert the measured voltage level into a
> measured power level, and the reference voltage level into a reference
> power level.
>
> Here is where the shortcut comes in, but remember, dB's always compare
> power levels. *It is the definition.
>
> But when you are comparing voltage levels, it turns out you get to use
> the trick of multiplying by 20*log(ratio) instead of 10*log(ratio),
> becuase power proportional to the voltage squared. *so 10*log(V1^2/
> V2^2) is the same as
>
> 20*log(V1/V2). *This is a shortcut or trick. Always go back to dB's
> compare power per the definition formula 10*log(P1/P2).
>
> The 20 log thing comes into play becuase in the real world you rarely
> measure power directly. *You measure voltages directly, and then
> apply the 20* trick to convert the voltages to power.- Hide quoted text -
>
> - Show quoted text -


PS I have a website that describes some DSP stuff. One of the
programs that I wrote gives an overview of dB's as a precurser to
understanding windowing.

Look it over if you like. The dB stuff is on the first and especially
second page of the program.

http://www.fourier-series.com/fourie...ows/index.html

On Oct 7, 9:14*pm, Randy Yates <ya...@ieee.org> wrote:
> glen herrmannsfeldt <g...@ugcs.caltech.edu> writes:
> > Richard Owlett wrote:
>
> >> c...@claysturner.com in *ERRROOOORRRR* wrote:
>
> >>> Even in acoustics, we have 100 dB is 0.946 watts per square meter.
>
> >> I would agree IF *and only* IF you stated dbV, dbm, or db.... with
> >> stated/implied load/impedance/****
>
> > I presume that is for a propagating wave in air. *The actual power
> > that goes into some detector (or other medium) depends on the
> > impedance in that medium.
>
> But it's just like the electrical situation - if we assume the
> same impedance for the reference as for the measured signal,
> the two cancel and don't really matter - we can compute it from
> the amplitudes (or equivalently, sound intensities).
>
> I think Richard is right. I think what Clay meant was 100 dB SPL.
> --
> % *Randy Yates * * * * * * * * *% "Watching all the days go by... * *
> %% Fuquay-Varina, NC * * * * * *% *Who are you and who am I?"
> %%% 919-577-9882 * * * * * * * *% 'Mission (A World Record)',
> %%%% <ya...@ieee.org> * * * * * % *A New World Record*, ELOhttp://www.digitalsignallabs.com

Well when one talks about sound, db specifically refers to sound
pressure level - that is why one doesn't need the "m" or something
else to designate the reference power. Yes one may add the "SPL" to
reduce ambiguity.

Instead of so many watts per square meter, when can equivalently give
a reference in terms of pascals which is simply newtons per square
meter.

As like with the electrical case, the reference units cancel - they
must cancel infact. Arguments of transcendental functions must be
unitless!

Clay

[email protected] wrote:
> On Oct 7, 9:14 pm, Randy Yates <ya...@ieee.org> wrote:
> Well when one talks about sound, db specifically refers to sound
> pressure level - that is why one doesn't need the "m" or something
> else to designate the reference power. Yes one may add the "SPL" to
> reduce ambiguity.

I suggest it's all the same whether it's sound or radar or electrical
signals or ... you name it.

There is almost always a "standard" reference. With the standard reference
people just stop saying: "referenced to....(whatever)"
Referenced to a milliwatt as in dBm,
Referenced to 1vrms (which can conjure up the impedance level if the
reference AND the measurement don't match up in that regard).
Referenced to 1 micropascal (generally used in water)
Referenced to 20 micropascals (generally used in air)
Reference to 1 newton/sq meter
etc. etc.

So, if you're going to say "SPL" then I would ask right away:
in air or in water?

Fred

[email protected] writes:

> On Oct 7, 9:14*pm, Randy Yates <ya...@ieee.org> wrote:
>> glen herrmannsfeldt <g...@ugcs.caltech.edu> writes:
>> > Richard Owlett wrote:
>>
>> >> c...@claysturner.com in *ERRROOOORRRR* wrote:
>>
>> >>> Even in acoustics, we have 100 dB is 0.946 watts per square meter.
>>
>> >> I would agree IF *and only* IF you stated dbV, dbm, or db.... with
>> >> stated/implied load/impedance/****
>>
>> > I presume that is for a propagating wave in air. *The actual power
>> > that goes into some detector (or other medium) depends on the
>> > impedance in that medium.
>>
>> But it's just like the electrical situation - if we assume the
>> same impedance for the reference as for the measured signal,
>> the two cancel and don't really matter - we can compute it from
>> the amplitudes (or equivalently, sound intensities).
>>
>> I think Richard is right. I think what Clay meant was 100 dB SPL.
>> --
>> % *Randy Yates * * * * * * * * *% "Watching all the days go by... * *
>> %% Fuquay-Varina, NC * * * * * *% *Who are you and who am I?"
>> %%% 919-577-9882 * * * * * * * *% 'Mission (A World Record)',
>> %%%% <ya...@ieee.org> * * * * * % *A New World Record*, ELOhttp://www.digitalsignallabs.com
>

Hi Clay,

> Well when one talks about sound, db specifically refers to sound
> pressure level -

I agree with that ...

> that is why one doesn't need the "m" or something else to designate
> the reference power.

Well, if you don't, then the reference power is unknown.

That's why stating (even within the context of sound power) "100 dB is
0.946 watts per square meter" isn't really correct, just as stating "100
dB is 39.2 watts into the load" would not really be correct. It isn't
absolute power unless the reference power is explicit, and with a simple
"dB", the reference power isn't explicit.

Every time someone uses the "naked" term "dB", the reference level has
been somehow specified in the context; e.g., "My satellite LNA output
power level is 4 dB higher than it was yesterday."
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% <[email protected]> % 'Yours Truly, 2095', *Time*, ELO
http://www.digitalsignallabs.com

On Oct 8, 12:39*pm, Randy Yates <ya...@ieee.org> wrote:
> c...@claysturner.com writes:
> > On Oct 7, 9:14*pm, Randy Yates <ya...@ieee.org> wrote:
> >> glen herrmannsfeldt <g...@ugcs.caltech.edu> writes:
> >> > Richard Owlett wrote:
>
> >> >> c...@claysturner.com in *ERRROOOORRRR* wrote:
>
> >> >>> Even in acoustics, we have 100 dB is 0.946 watts per square meter.
>
> >> >> I would agree IF *and only* IF you stated dbV, dbm, or db.... with
> >> >> stated/implied load/impedance/****
>
> >> > I presume that is for a propagating wave in air. *The actual power
> >> > that goes into some detector (or other medium) depends on the
> >> > impedance in that medium.
>
> >> But it's just like the electrical situation - if we assume the
> >> same impedance for the reference as for the measured signal,
> >> the two cancel and don't really matter - we can compute it from
> >> the amplitudes (or equivalently, sound intensities).
>
> >> I think Richard is right. I think what Clay meant was 100 dB SPL.
> >> --
> >> % *Randy Yates * * * * * * * * *% "Watching all the days go by... * *
> >> %% Fuquay-Varina, NC * * * * * *% *Who are you and who am I?"
> >> %%% 919-577-9882 * * * * * * * *% 'Mission (A World Record)',
> >> %%%% <ya...@ieee.org> * * * * * % *A New World Record*, ELOhttp://www.digitalsignallabs.com
>
> Hi Clay,
>
> > Well when one talks about sound, db specifically refers to sound
> > pressure level -
>
> I agree with that ...
>
> > that is why one doesn't need the "m" or something else to designate
> > the reference power.
>
> Well, if you don't, then the reference power is unknown.
>
> That's why stating (even within the context of sound power) "100 dB is
> 0.946 watts per square meter" isn't really correct, just as stating "100
> dB is 39.2 watts into the load" would not really be correct. It isn't
> absolute power unless the reference power is explicit, and with a simple
> "dB", the reference power isn't explicit.
>

In the case of sound, which is a perceptual thing involving humans,
the reference is found emperically. The standard way is to fill a room
with people around the age of 21 years and play a 1000 Hz sound
starting from almost absoulute quiet until about 1/2 of the group can
detect the sound. Guys in the 30 to 40 year old range need 2 to 3
times as much acoustic energy as the younger set to just make
threshold of detection, and it gets worse from there as one ages.


As I alluded to earlier 100 dB SPL being 0.946 watts per square meter
is the resulting experimental value that corresponds to 0 dB being the
threshold of human detection. So if I say a sound has a level of
100dB, I'm not talking about a signal in a wire or such. I'm talking
about the strength of the acoustic vibrations in the atmosphere at
STP. The reason I bring this up is this is the case where we don't
need to use a reference since sound is perceptual and therefore the
reference is humans.

Many units have built in to them a customary method of measurement.

This is highlighted by the old riddle of what weights more: an ounce
of gold or and ounce of lead? Well we know the trick's answer is an
ounce of gold. Precious metals are measured in troy ounces which are
1/14th of a pound. Other things are in avoirdupois ounces which are
1/16th of a pound. So the reference here is linked to what we are
talking about. Sound levels imply SPL.

IHTH,
Clay

[email protected] wrote:

...

> As I alluded to earlier 100 dB SPL being 0.946 watts per square meter
> is the resulting experimental value that corresponds to 0 dB being the
> threshold of human detection. So if I say a sound has a level of
> 100dB, I'm not talking about a signal in a wire or such. I'm talking
> about the strength of the acoustic vibrations in the atmosphere at
> STP. The reason I bring this up is this is the case where we don't
> need to use a reference since sound is perceptual and therefore the
> reference is humans.

With regret, no. the reference is the sound power level at which 50$ og
the test subjects become aware of the sound. Your 100 dB is still a
ratio: 10^10 times the reference.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
** Posted from http://www.teranews.com **

On Oct 8, 1:44*pm, Jerry Avins <j...@ieee.org> wrote:
> c...@claysturner.com wrote:
>
> * *...
>
> > As I alluded to earlier 100 dB SPL being 0.946 watts per square meter
> > is the resulting experimental value that corresponds to 0 dB being the
> > threshold of human detection. So if I say a sound has a level of
> > 100dB, I'm not talking about a signal in a wire or such. I'm talking
> > about the strength of the acoustic vibrations in the atmosphere at
> > STP. The reason I bring this up is this is the case where we don't
> > need to use a reference since sound is perceptual and therefore the
> > reference is humans.
>
> With regret, no. the reference is the sound power level at which 50$ og
> the test subjects become aware of the sound. Your 100 dB is still a
> ratio: 10^10 times the reference.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
> ** Posted fromhttp://www.teranews.com**

I said it corresponds to not is equal to. That's why there is an
offset of 100dB. I didn't imply that 0.946 watts/meter^2 is 0dB, it is
100dB. I'm sorry if my poor wording made matters confusing. 0 dB is
0.946E-10 watts/meter^2 If you figure the average eardrum to have an
area of about 0.5*10E-4 m^2, then at 0 dB, the energy captured by the
ear at the threshold of detection is down in the femtowatt range -
damn sensitive!!! This turns out to be not very far from the noise
floor in the ear due to brownian motion and turbulant bloodflow.

IHTH,

Clay



Clay

hi, i don't know why this is being made so complicated...

> 10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)
>
> They say it is often used in electronics to compare voltages, but why is
> it used in digital audio? Yeah I know that the digital values are
> equivalent to resulting electrical power, but we are not comparing anything
> to anything. So why should we square?

because the square of the amplitude is proportional to the power
carried by the sound wave.
dB is a measure of relative powers.
power also correlates better to perceived loudness.

> And if so, then when should we NOT square?

when measuring loudness, never that i can think of.

forget all this stuff about SPL reference points or whatever, it's
irrelevant since you're not measuring anything in the real world.
(pick away...)

[email protected] wrote:
> On Oct 8, 1:44 pm, Jerry Avins <j...@ieee.org> wrote:
>> c...@claysturner.com wrote:
>>
>> ...
>>
>>> As I alluded to earlier 100 dB SPL being 0.946 watts per square meter
>>> is the resulting experimental value that corresponds to 0 dB being the
>>> threshold of human detection. So if I say a sound has a level of
>>> 100dB, I'm not talking about a signal in a wire or such. I'm talking
>>> about the strength of the acoustic vibrations in the atmosphere at
>>> STP. The reason I bring this up is this is the case where we don't
>>> need to use a reference since sound is perceptual and therefore the
>>> reference is humans.
>> With regret, no. the reference is the sound power level at which 50$ og
>> the test subjects become aware of the sound. Your 100 dB is still a
>> ratio: 10^10 times the reference.

...

> I said it corresponds to not is equal to. That's why there is an
> offset of 100dB. I didn't imply that 0.946 watts/meter^2 is 0dB, it is
> 100dB. I'm sorry if my poor wording made matters confusing. 0 dB is
> 0.946E-10 watts/meter^2 If you figure the average eardrum to have an
> area of about 0.5*10E-4 m^2, then at 0 dB, the energy captured by the
> ear at the threshold of detection is down in the femtowatt range -
> damn sensitive!!! This turns out to be not very far from the noise
> floor in the ear due to brownian motion and turbulant bloodflow.

I evidently smeared egg on my face by not reading carefully. It
nevertheless remains true that SPL given in dB remains a ratio, which
was my point.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
** Posted from http://www.teranews.com **

On Oct 8, 2:33*pm, Jerry Avins <j...@ieee.org> wrote:
> c...@claysturner.com wrote:
> > On Oct 8, 1:44 pm, Jerry Avins <j...@ieee.org> wrote:
> >> c...@claysturner.com wrote:
>
> >> * *...
>
> >>> As I alluded to earlier 100 dB SPL being 0.946 watts per square meter
> >>> is the resulting experimental value that corresponds to 0 dB being the
> >>> threshold of human detection. So if I say a sound has a level of
> >>> 100dB, I'm not talking about a signal in a wire or such. I'm talking
> >>> about the strength of the acoustic vibrations in the atmosphere at
> >>> STP. The reason I bring this up is this is the case where we don't
> >>> need to use a reference since sound is perceptual and therefore the
> >>> reference is humans.
> >> With regret, no. the reference is the sound power level at which 50$ og
> >> the test subjects become aware of the sound. Your 100 dB is still a
> >> ratio: 10^10 times the reference.
>
> * *...
>
> > I said it corresponds to not is equal to. That's why there is an
> > offset of 100dB. I didn't imply that 0.946 watts/meter^2 is 0dB, it is
> > 100dB. I'm sorry if my poor wording made matters confusing. 0 dB is
> > 0.946E-10 watts/meter^2 If you figure the average eardrum to have an
> > area of about 0.5*10E-4 m^2, then at 0 dB, the energy captured by the
> > ear at the threshold of detection is down in the femtowatt range -
> > damn sensitive!!! This turns out to be not very far from the noise
> > floor in the ear due to brownian motion and turbulant bloodflow.
>
> I evidently smeared egg on my face by not reading carefully. It
> nevertheless remains true that SPL given in dB remains a ratio, which
> was my point.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
> ** Posted fromhttp://www.teranews.com**- Hide quoted text -
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> - Show quoted text -

I agree that there is an implicit ratio since a log(0) raises issues
in terms of doing some kind of measurement. I was trying to get at the
fact that we don't put an additional letter to denote the reference
such as the case with dBm and dBw.

Clay

[email protected] writes:
> [...]
> 0 dB is 0.946E-10 watts/meter^2

Zicker and Fastl says it's 10^(-12) W/m^2 (p.1).

@BOOK{psychoacoustics,
title = "{Psychoacoustics: Facts and Models}",
author = "E.~Zwicker and H.~Fastl",
publisher = "Springer",
edition = "second",
year = "1999"}
--
% Randy Yates % "So now it's getting late,
%% Fuquay-Varina, NC % and those who hesitate
%%% 919-577-9882 % got no one..."
%%%% <[email protected]> % 'Waterfall', *Face The Music*, ELO
http://www.digitalsignallabs.com

[email protected] writes:
> [...]
> I was trying to get at the fact that we don't put an additional letter
> to denote the reference such as the case with dBm and dBw.

Hi Clay,

I don't know why you would assert such a thing. I don't agree.

There are multiple reference levels, even within the context of
acoustics, and even within the context of acoustics for humans.

In both cases, the expression determining dB is

dB = 20 * log_10 (p / p_ref),

The first reference level is dB SPL, which is mentioned in other posts,
in which p_ref = 0.0002 microbar (2E-5 newton/m^2). This also
corresponds to an intensity of 10^(-12) W/m^2.

The second does not have a special acronym or identification
but it is p_ref = 1 microbar.

I quote these from Baranek.

Baranek concludes the paragraph with the statement

"The reference pressure must always be stated explicitly."

Unless I'm misunderstanding you, this would seem to diametrically
contradict your assertion.

--Randy


@book{baranek,
title = "Acoustics",
author = "{Leo L. Baranek}",
publisher = "McGraw-Hill",
year = "1954"}

--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <[email protected]> % 'Yours Truly, 2095', *Time*, ELO
http://www.digitalsignallabs.com

Randy Yates <[email protected]> writes:

> [email protected] writes:
>> [...]
>> 0 dB is 0.946E-10 watts/meter^2
>
> Zicker

Doh! Zwicker!!!

> and Fastl says it's 10^(-12) W/m^2 (p.1).
> @BOOK{psychoacoustics,
> title = "{Psychoacoustics: Facts and Models}",
> author = "E.~Zwicker and H.~Fastl",
> publisher = "Springer",
> edition = "second",
> year = "1999"}

--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% <[email protected]> % 'Living' Thing', *A New World Record*, ELO
http://www.digitalsignallabs.com

"jungledmnc" <[email protected]> writes:

> Hi,
> this question might be very trivial, but I haven't found good explanation
> anywhere else.
>
> I have an audio signal - some sine. Use a wavelabl to look at the
> waveform, and its maximum is at about 0.6. When I change the display into
> dB it shows about -5dB at that level.
> But this does not make sense - the formula is 10*log10(amplitude).

No. The formula is

dB = 10 * log10(P / P_ref) [1]

> So it should be -2.5dB.

No, 0.6 V peak should be about -4.44 dB.

> I have found, that this is because we use squares for comparison : 10
> * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)

Right equation, wrong reason. We use squares for voltages (or
amplitudes, as you call them) because the decibel formula ALWAYS relates
two powers (see equation [1]), and power is related to the square of
voltage.

Since P = V^2 / R, then if the two powers (P and P_ref) both have the
same resistance R, then we can also compare voltages using dB.

> They say it is often used in electronics to compare voltages, but why is
> it used in digital audio? Yeah I know that the digital values are
> equivalent to resulting electrical power, but we are not comparing anything
> to anything.

You are, by definition, comparing one power level to a reference power
level. That is the DEFINITION of dB (see equation [1]).

> So why should we square?

Because we're always comparing powers (see equation [1]).

> And if so, then when should we NOT square?

As you already know, one property of logarithms is that log(x^y) = y *
log(x). Since P = V^2 / R, then if P and P_ref in equation [1] are
both at the same resistance R, then

dB = 10 * log10( (V^2 / R) / (V_ref^2 / R) )
= 10 * log10( V^2 / V_ref^2 )
= 10 * log10( (V / V_ref)^2 )
= 20 * log10( V / V_ref ). [2]

So, even though you're computing the ratio of two powers, you can
equivalently use equation [2] when the impedance of the two powers
are the same.

Now to get to your root question, in digital audio we're often concerned
about how close a signal is to full-scale. So when we compute a decibel
value for a digital audio signal, we commonly make the following
assumptions:

1. The range of digital amplitudes are between +1 and -1. That is, any
sample x[n] is in the range -1 <= x[n] <= +1.

2. The amplitude represents voltage (or current).

3. Even though this is a digital signal and has nothing to do with a
physical quantity, we assume there is a resistance involved and,
further, that the resistance is the same as the reference resistance.

4. The reference power is assumed to be the RMS power of a full-scale
sine wave. Thus, V_ref = sqrt(2) / 2 VRMS, or simply 1 Vpeak.

Thus your 0.6 Vpeak signal is 20 * log10(0.6 / 1) ~= -4.44 dBFS, which
means it is 4.44 dB below full-scale.
--
% Randy Yates % "My Shangri-la has gone away, fading like
%% Fuquay-Varina, NC % the Beatles on 'Hey Jude'"
%%% 919-577-9882 %
%%%% <[email protected]> % 'Shangri-La', *A New World Record*, ELO
http://www.digitalsignallabs.com

Randy Yates <[email protected]> writes:
> [...]

PS: See here for a great old exposition on decibels.

http://www.digitalsignallabs.com/doc/db.pdf

(Caveat: this file is scanned and is a little big - 2.4 MB).
--
% Randy Yates % "Bird, on the wing,
%% Fuquay-Varina, NC % goes floating by
%%% 919-577-9882 % but there's a teardrop in his eye..."
%%%% <[email protected]> % 'One Summer Dream', *Face The Music*, ELO
http://www.digitalsignallabs.com

On Oct 8, 4:41*pm, Randy Yates <ya...@ieee.org> wrote:
> c...@claysturner.com writes:
> > [...]
> > I was trying to get at the fact that we don't put an additional letter
> > to denote the reference such as the case with dBm and dBw.
>
> Hi Clay,
>
> I don't know why you would assert such a thing. I don't agree.
>
> There are multiple reference levels, even within the context of
> acoustics, and even within the context of acoustics for humans.
>
> In both cases, the expression determining dB is
>
> * dB = 20 * log_10 (p / p_ref),
>
> The first reference level is dB SPL, which is mentioned in other posts,
> in which p_ref = 0.0002 microbar (2E-5 newton/m^2). This also
> corresponds to an intensity of 10^(-12) W/m^2.
>
> The second does not have a special acronym or identification
> but it is p_ref = 1 microbar.
>
> I quote these from Baranek.
>
> Baranek concludes the paragraph with the statement
>
> * "The reference pressure must always be stated explicitly."
>
> Unless I'm misunderstanding you, this would seem to diametrically
> contradict your assertion.
>
> --Randy
>
> @book{baranek,
> * title = "Acoustics",
> * author = "{Leo L. Baranek}",
> * publisher = "McGraw-Hill",
> * year = "1954"}
>
> --
> % *Randy Yates * * * * * * * * *% "Maybe one day I'llfeel her cold embrace,
> %% Fuquay-Varina, NC * * * * * *% * * * * * * ** * *and kiss her interface,
> %%% 919-577-9882 * * * * * * * *% * * * * * *til then, I'll leave her alone."
> %%%% <ya...@ieee.org> * * * * * % * * * *'Yours Truly, 2095', *Time*, ELO *http://www.digitalsignallabs.com

Certainly, the plethora of difference refernce values, would indicate
one should state which reference he is using. When I get back to the
farm, I have an old book, "The Science of Measurement," which has a
couple of chapters on sound measurements. I'll review it and see how
its author denotes the different reference values. This book is good
about giving the historical basis behind various units and how they
sometimes get redefined over time. Sometimes they get rounded to some
nearest convenient value. A kT TNT energy equivalent is one such
example. It is taken to be 10^12 calories which is a value very close
to experimental values for TNT. I'll report what I find out about
the sound measurements.

Clay

On Oct 8, 4:11 pm, c...@claysturner.com wrote:

> I agree that there is an implicit ratio since a log(0) raises issues
> in terms of doing some kind of measurement.

Nope. That's not the problem.

> I was trying to get at the
> fact that we don't put an additional letter to denote the reference
> such as the case with dBm and dBw.

You're doing it wrong.

You cannot measure anything with a dimensionless number, which is what
dB is. You can only measure the ratio between two somethings, and you
have to state what the reference one is. It matter's not a bit that
your reference is people, you still have to state it.

[email protected] wrote:
> On Oct 8, 4:11 pm, c...@claysturner.com wrote:
>
>> I agree that there is an implicit ratio since a log(0) raises issues
>> in terms of doing some kind of measurement.
>
> Nope. That's not the problem.
>
>> I was trying to get at the
>> fact that we don't put an additional letter to denote the reference
>> such as the case with dBm and dBw.
>
> You're doing it wrong.
>
> You cannot measure anything with a dimensionless number, which is what
> dB is. You can only measure the ratio between two somethings, and you
> have to state what the reference one is. It matter's not a bit that
> your reference is people, you still have to state it.

power/people is not dimensionless.

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