Why dB ?

Hello,

I am wondering that why we do have dB to represent the gain of 
the signal, for example we can say that the gain is 70% .. 50% 
or maybe 12.5 ..etc. There should be one special reason that we 
have to use dB. Could you tell me what it is ? (I am still 
a student and DSP a little bit new to me, so forgive me if 
I ask so simple questions :D)

Thank you very much,                                

-------
Phong [Zeronen]

Le Phong wrote:
> Hello,
> 
> I am wondering that why we do have dB to represent the gain of 
> the signal, for example we can say that the gain is 70% .. 50% 
> or maybe 12.5 ..etc. There should be one special reason that we 
> have to use dB. Could you tell me what it is ? (I am still 
> a student and DSP a little bit new to me, so forgive me if 
> I ask so simple questions :D)
> 
> Thank you very much,                                
> 
> -------
> Phong [Zeronen]

For the same reason you sometimes plot data on a logarithmic scale. 
Since the strengths of signals can vary over many orders of magnitudes, 
a logarithmic scale keeps the numbers "nice". A good analogy is the 
Richter scale used to quantify earthquakes.

OUP

"Le Phong" <lphong@ruutana.ratol.fi> wrote in message
news:c6bi5l$qjj$1@news.oamk.fi...
> Hello,
>
> I am wondering that why we do have dB to represent the gain of
> the signal, for example we can say that the gain is 70% .. 50%
> or maybe 12.5 ..etc. There should be one special reason that we
> have to use dB. Could you tell me what it is ? (I am still
> a student and DSP a little bit new to me, so forgive me if
> I ask so simple questions :D)
>
> Thank you very much,
>
> -------
> Phong [Zeronen]

Hello Le Phong,

When we consider the affects of multiple gains on a signal, to find the
total gain, we have to multiply the gains of each of the affecting factors.
But with a logarithmic representation, we simply add together - much easier.

Even with RF where a power law (remember the inverse square law for signals
in space where the energy is conserved) works well to describe the signal
strength as a function of distance. Well in a logarithmic representation a
power law simply becomes x db of loss per unit distance.

So using dB is certainly a matter of convenience, However when signals have
a large dynamic range, the logarithmic representation is also easier to work
with.

For example a cellphone may transmit at 0.6 watts. And a minimal signal to a
cellphone is 0.000 000 000 000 002 watts! In db notation (referenced to a
milliwatt) these levels are approximately +27dBm and -117dBm.

And this brings up a point of common misconception. A gain or loss can be
simply stated as being so many dB. However an actual power level when stated
in dB is in reference to a standard power. The 'm' in dBm means the
reference is 1mW. Likewise dBw is relative to one watt. Now sound pressure
levels are given as just dB, and there is also a standard reference. IIRC
100dB spl (sound pressure level) is 0.937 watts per square meter. dB as used
with human hearing gets complicated in that we don't hear all frequencies
equally well and even their perceived relative levels is overall level
dependent.

I hope this helps some.

Clay

-- 
Clay S. Turner, V.P.
Wireless Systems Engineering, Inc.
Satellite Beach, Florida 32937
(321) 777-7889
www.wse.biz
csturner@wse.biz

Le Phong wrote:
> Hello,
> 
> I am wondering that why we do have dB to represent the gain of 
> the signal, for example we can say that the gain is 70% .. 50% 
> or maybe 12.5 ..etc. There should be one special reason that we 
> have to use dB. Could you tell me what it is ? (I am still 
> a student and DSP a little bit new to me, so forgive me if 
> I ask so simple questions :D)
> 
> Thank you very much,                                
> 
> -------
> Phong [Zeronen]

It's not hard to convert decibels to percent and percent to decibels.
There are several things that make decibels convenient.

Decibels are logarithmic, so the range of numbers needed to express a
range of powers is smaller than with percentages, and so easier to
comprehend. For example, -40 to +40 dB represents .1/10,000 to 10,000.

To compute the result of cascaded operations, one can add decibels, but
one needs to multiply percentages.

For many systems, plots of response in dB vs. log frequency is nearly a
straight line in interesting regions. The slope of the line and the
frequencies where it changes provide useful system information.

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

Apart from the engineering arguments already posted, there is a more fundamental 
reason, and it is the same reason musicians use a logarithmic scale for 
frequency (i.e. semitones, octaves etc): the log scale more closely matches how 
we hear. The maths arguments would not hold so strongly were it not for this. As 
a rough rule of thumb, the smallest level difference that can be discriminated 
by the ear is around 0.5dB (but this can depend on the characteristics of the 
signal). A cut of 50% on an amplitude scale sounds like a lot ("reducing the 
level by a half!"), but this only amounts to a drop of 6dB, which is not really 
that much, relative to the whole hearing range. If you were asked to reduce the 
volume of a sound "by half", the chances are you would drop it by much more than 
6dB.

Similarly, we are much more comfortable dealing with constant intervals ("octave 
up, fifth down"), than with raw frequency factors ("double", "two-thirds"). So, 
   viewed purely in an everyday sense, you could think of the dB unit as a 
counterpart to the semitone (say).


Richard Dobson

Le Phong wrote:

> Hello,
> 
> I am wondering that why we do have dB to represent the gain of 
> the signal, for example we can say that the gain is 70% .. 50% 
> or maybe 12.5 ..etc. There should be one special reason that we 
> have to use dB. Could you tell me what it is ? (I am still 
> a student and DSP a little bit new to me, so forgive me if 
> I ask so simple questions :D)
> 
> Thank you very much,                                
> 
> -------
> Phong [Zeronen]

"Jerry Avins" <jya@ieee.org> wrote in message
news:408969a5$0$28906$61fed72c@news.rcn.com...
>
> For many systems, plots of response in dB vs. log frequency is nearly a
> straight line in interesting regions. The slope of the line and the
> frequencies where it changes provide useful system information.
>

A great observation.  Many physical systems have exponential changes with
time or with frequency.  Since logarithms often simplify exponential
representations - it's a natural application.

I guess we no longer view multiplication as harder to do than addition
because of electronic calculators and spread sheets .. so I was going to say
that that advantage of long standing is probably a bit less important.

Well ... that is ... until I realized that things like the sonar equation,
radar equation, etc. would probably be harder to work with - where one is
doing symbolic manipulation and pondering system elements and their
contribution to performance.

Fred

In article 408969a5$0$28906$61fed72c@news.rcn.com, Jerry Avins at
jya@ieee.org wrote on 04/23/2004 15:08:

> Le Phong wrote:
>> Hello,
>> 
>> I am wondering that why we do have dB to represent the gain of
>> the signal, for example we can say that the gain is 70% .. 50%
>> or maybe 12.5 ..etc. There should be one special reason that we
>> have to use dB. Could you tell me what it is ?

the fundamental reason for using a logarithmic scale for loudness is that
the amount of perceived loudness gain going from 50 watts to 100 watts is
the same perceived loudness gain going from 100 watts to 200 watts.  at
least that is the case for a range of frequencies and power intensity
levels.

why dB instead of base10 log units (called "bels")?  or base e log units
(called "nepers")?  because a decibel corresponds to a barely perceptible
increase in loudness for most people with good hearing (check out the
Fletcher-Munson curves).

>> Thank you very much,

FWIW.

> It's not hard to convert decibels to percent and percent to decibels.
> There are several things that make decibels convenient.

i wish we defined percent change in a log way:

    % change = ln(after/before) * 100%

instead of the conventional way:

   % change = (after - before)/before * 100%

that way a 10% increase followed by a 10% loss would bring you exactly back
to where you begun.

so if we change that and MATLAB's indexing (and ditch the Abomination in the
White House), life would have more justice.

r b-j

Hi Le Phong : it's basically that you want a measure that is pretty well
independent of the impdedance in the medium you propagate your signal
through , so comparison of powers is good.  Once you agree to compare powers
then it's nice to have something that conveniently covers a large dynamic
range ,  say something from noise power in 1 Hz at 4K to several gigawatts
and the result is that you express your power comparison logarithmically in
Bels, deciBels or nepers.

Best of  luck - Mike

"Le Phong" <lphong@ruutana.ratol.fi> wrote in message
news:c6bi5l$qjj$1@news.oamk.fi...
> Hello,
>
> I am wondering that why we do have dB to represent the gain of
> the signal, for example we can say that the gain is 70% .. 50%
> or maybe 12.5 ..etc. There should be one special reason that we
> have to use dB. Could you tell me what it is ? (I am still
> a student and DSP a little bit new to me, so forgive me if
> I ask so simple questions :D)
>
> Thank you very much,
>
> -------
> Phong [Zeronen]

Richard Dobson wrote:

> Apart from the engineering arguments already posted, there is a more 
> fundamental reason

Read again the original post -- we're not comparing geometric vs.
arithmetic;  we're comparing two types of geometric measures  (the
OP specifically asked why log instead of percentages, or ratios
in general).

That fundamental reason you're talking about does not specifically
explain why we use logarithmic scale -- the reason [for logarithmic
scale] is purely mathematical  (addition instead of multiplication,
larger range covered with manageable numbers, etc.)

Carlos
--

Richard Dobson wrote:
> Apart from the engineering arguments already posted, there is a more 
> fundamental reason, and it is the same reason musicians use a 
> logarithmic scale for frequency (i.e. semitones, octaves etc): the log 
> scale more closely matches how we hear. The maths arguments would not 
> hold so strongly were it not for this. As a rough rule of thumb, the 
> smallest level difference that can be discriminated by the ear is around 
> 0.5dB (but this can depend on the characteristics of the signal). A cut 
> of 50% on an amplitude scale sounds like a lot ("reducing the level by a 
> half!"), but this only amounts to a drop of 6dB, which is not really 
> that much, relative to the whole hearing range. If you were asked to 
> reduce the volume of a sound "by half", the chances are you would drop 
> it by much more than 6dB.
> 
> Similarly, we are much more comfortable dealing with constant intervals 
> ("octave up, fifth down"), than with raw frequency factors ("double", 
> "two-thirds"). So,   viewed purely in an everyday sense, you could think 
> of the dB unit as a counterpart to the semitone (say).
> 
> 

I understand octave(s).
Can someone give me a mathmatical definition of semitone?

A Google seach said essentially "smallest frequency interval used by 
western musicians".

Another reference said a semitone was the smallest frequency 
difference the average person could distinguish.