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A Decibel = Primer Studio = Overviews
Posted by CapnZilog - Oct = 27, 2006=20 @ 09:00:51 PM  


A short but deep = exploration of=20 recording's most confusing subject

(for=20 a more readable and properly formatted version, please = visit:=20 = http://dallashodgson.info/files/DecibelPrimer.pdf)
<= BR>A=20 Decibel Primer

Dallas=20 = Hodgson
10/23/06
v1.2

In=20 all the world of audio, there is no measurement that = is so=20 key, yet so difficult to understand, than the decibel = (dB.)=20 They=EF=BF=BDre so commonly used both in live sound = and recording that=20 we often take them for granted without understanding = they=20 really mean or worse, understanding them incorrectly. = And it=EF=BF=BDs=20 very easy to understand them incorrectly, because = there are=20 many flavors of dB (which we=EF=BF=BDll get to in a = moment) and=20 without the proper frame of reference, are as = meaningless as=20 they are convenient. But audio convenience is at the = heart of=20 all this, because the decibel scale would not exist = were it=20 not for Alexander Graham Bell, inventor of the = telephone=20 (which it was named after.)

Part of the reason = for the=20 decibel scale, which is derived from logarithms, is to = compress the extreme range of loudness perceivable by = the=20 human ear into something more = compact.

(threshold of=20 hearing/pain chart derived from=20 http://ohioline.osu.edu/cd-fact/0190.html, Dave = Moulton and=20 myself)

Safe Range (dB SPL) Sound Pressure = Ratio over=20 0dB (times)

Threshold of Hearing (.0002 = dynes/cm^2) 0=20 dB 1 x
(convenient reference) 6.02 dB 2 = x
(convenient=20 reference) 10 dB 3.16 x
Stream flow, rustling = leaves 15 dB=20 5.62 x
Watch ticking 20 dB 10 x
Soft whisper 30 = dB 32=20 x
Quiet street noises 40 dB 100 x
Conversation, = quiet=20 room 45 dB 178 x
Conversation, crowded room 60 dB = 1,000 x=20
Normal city or freeway traffic 70 dB 3,162 x =
Vacuum=20 cleaner 75 dB 5,623 x
Hair dryer 80 dB 10,000=20 x
Motorcycle, electric shaver 85 dB 17,783 = x
Lawn mower,=20 heavy equipment 90 dB 31,623 x
Garbage truck 100 dB = 100,000=20 x
Screaming baby 115 dB 562,341 x

Injury = Range (dB=20 SPL) Sound Pressure Ratio over 0dB (times)

Jack = hammer=20 3 feet /
Jet airplane takeoff from 120 feet = /
Threshold=20 of discomfort 120 dB 1,000,000 x
Air begins to = distort 125=20 dB 1,778,279 x
Race car, loud thunder, rock band = 120-130 dB=20 1,000,000 x - 3,162,278 x
Sensation of eardrums = moving=20 (=EF=BF=BDtickle=EF=BF=BD) 130 dB 3,162,278 = x
=EF=BF=BDHorrific=EF=BF=BD Pain 140 dB=20 10,000,000 x
Rocket launch from 150 feet 180 dB=20 1,000,000,000 x
Theoretical maximum at 1 atmosphere = 194 dB=20 5,011,872,336 x

Some interesting things from = this table=20 =EF=BF=BD you can see that the human ear has a very = wide dynamic=20 range, with the loudest common sounds (120dB) being = one=20 million times louder in intensity (pressure) than the = quietest=20 sound we can hear. In fact, it is generally considered = that=20 for something to sound twice as loud to our ears its = SPL must=20 increase 20dB, a sound pressure increase of ten times. = You can=20 begin to see why faders on mixing boards are = calibrated in dB,=20 not sound pressure or volts; it would take a huge = fader to go=20 all the way from 0 to a million, and at low volumes = you=EF=BF=BDd be=20 moving the fader in impossibly small steps whereas at = high=20 volumes the hand motions required would be = huge.

Some=20 Interesting Sound Facts:

1) The ear is so = sensitive,=20 that if the Threshold of Hearing were much lower = we=EF=BF=BDd be=20 hearing the Brownian noise of air-molecules as they = randomly=20 bump into each other all day long.
2) I=EF=BF=BDve = also read the=20 Threshold Of Hearing being described as .0002 = microbars, 20=20 micropascals (=EF=BF=BDPa =3D 1=EF=BF=BD10^-6 Pa), = 10^-12 W/m^2 (watts per=20 square meter), and roughly the sound of a mosquito = flying 3=20 metres away!
3) Ever wonder why orchestras are so = large?=20 Because they need to be! It takes ten violinists to = sound=20 twice as loud as one (an increase of 20dB SPL.)
4) = Few=20 sounds in Nature (like lightning) are so loud that = that the=20 air itself distorts like a guitar amp. When a speaker = moves=20 forward, it creates air pressure; and when it moves = backward,=20 a partial vacuum. Now imagine a sound so large that = the=20 partial vacuum actually becomes total, and simply = can=EF=BF=BDt get=20 any larger =EF=BF=BD that=EF=BF=BDs what happens at = 194dB, and you=EF=BF=BDll probably=20 be dead - earplugs or not.
5) SPL stands for = =EF=BF=BDSound=20 Pressure Level=EF=BF=BD which is relative to the = threshold of hearing.=20 There are many other possible thresholds, such as = dbFS, dbM,=20 dbU, dbV and dbW which we=EF=BF=BDll get into later = but for now, just=20 remember that they=EF=BF=BDre all different beasts and = often can=EF=BF=BDt be=20 compared directly, like apples and oranges.
6) A 1 = dB=20 change in gain is about the smallest we can notice in=20 isolation. In the context of a mix though, .3dB-.5dB = changes=20 in gain are common for me. Professional recording = engineer=20 Roger Nichols has been known to make tweaks as small = as=20 .1dB!

The fact that the ear gets less sensitive = to=20 sounds as they get louder is by design. Internally, a = physical=20 mechanism actually =EF=BF=BDturns the volume = down=EF=BF=BD on the ear like a=20 compressor, but unfortunately this mechanism is not=20 instantaneous. One of the worst things you can do to = your ears=20 is to expose them to the sound of brief, impulsive = noises such=20 as explosions or gunfire. It may only last a fraction = of a=20 second, but an unexpected blast of 140dB SPL could = render you=20 deaf permanently. How about rock concerts? Well, at = least our=20 ears are somewhat prepared for that; but as = OSHA=EF=BF=BDs Table G-16=20 (below) shows, we can=EF=BF=BDt listen to loud sounds = forever without=20 sustaining some damage: (from=20 = http://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=3DSTANDARDS= &p_id=3D9736)

A-weighted=20 SPL (slow response) Max Recommended = Exposure

80dB 32=20 hrs
85dB 16 hrs
90dB 8 hrs
95dB 4 = hrs
100dB 2=20 hrs
105dB 1 hrs
110dB 30 min
115dB 15 = min
120dB 8=20 min
125dB 3.78 min
130dB 1.8 min

(Another = Factoid: =EF=BF=BDA-weighting=EF=BF=BD refers to one = of two common methods of=20 measuring sound with a sound level meter, the other = being=20 =EF=BF=BDC=EF=BF=BD-weighting. = =EF=BF=BDA=EF=BF=BD-weighting is less sensitive to low=20 frequencies, while the more accurate = =EF=BF=BDC=EF=BF=BD weighting is fairly=20 flat. For reasons that are unclear and probably have = to do=20 with lobbyists, =EF=BF=BDA=EF=BF=BD-weighting is the = preferred weighting in=20 laws regarding noise pollution.)

Note that 8 = min is not=20 a very long time to spend at a 120dB rock concert! = When you=20 leave the show, if you ears are ringing you have = received some=20 (possibly permanent) nerve damage which may degrade = your=20 ability to mix. So what level should one mix at? 85dB = is most=20 often cited as the ideal level. For one thing, your = ears can=20 tolerate a full day of it and secondly, the = ear=EF=BF=BDs=20 Fletcher-Munson frequency response (see=20 http://en.wikipedia.org/wiki/Fletcher-Munson_contours) = flattens out nicely giving you a more accurate read on = your=20 mix. Much louder than that? Wear earplugs! There are = some good=20 ones out there aimed at audiophiles and musicians that = sound=20 much better than what you=EF=BF=BDre probably used to, = and they=EF=BF=BDre a=20 very cheap investment for protecting your ears: See=20 http://www.etymotic.com/ephp/er20.aspx

This Is = Where It=20 Gets Tricky

So what makes  understanding = dB=EF=BF=BDs so=20 confusing? Part of it is that it=EF=BF=BDs not = intuitive to think in=20 terms of exponentials and logarithms. For example, = when I say=20 that in order to sound twice as loud it takes 10 times = the=20 sound pressure, expressed as an increase of 20dB, = that=EF=BF=BDs just=20 weird. So what do you get if you merely double the = sound=20 pressure? Only a 6.02dB increase, as it turns out. = 6.02dB is=20 one of those magic numbers that=EF=BF=BDs worth = memorizing (along with=20 20dB) because it comes up again and again in digital = audio.=20 Try this test:

1) Open up a project in SONAR, = find a=20 guitar track somewhere, and solo it. What=EF=BF=BDs = the highest peak=20 reported by the output bus meter? Let=EF=BF=BDs say = it=EF=BF=BDs =EF=BF=BD10dB.
2)=20 Clone that guitar track, solo it, and play both tracks = at the=20 same time. What=EF=BF=BDs the highest peak reported by = the output bus=20 meter now?

I don=EF=BF=BDt even have to look to = know =EF=BF=BD it=EF=BF=BDs=20 around =EF=BF=BD4dB, which is ~6dB louder than what = you got by playing=20 the single track alone. Why? Because you=EF=BF=BDve = just doubled the=20 sound intensity by playing two identical guitars at = the same=20 time. OK, now you should be able to figure this out = =EF=BF=BD what if=20 you wanted to make a single guitar sound twice as = loud? You=EF=BF=BDd=20 make 8 more copies (for a total of 10) and = play=EF=BF=BDem all at once=20 =EF=BF=BD this yields a 20dB increase, but be careful = at this point=20 because your output meters will be clipping severely! = Why?=20 Because =EF=BF=BD10dB + 20dB =3D 10dB, which is 10dB = over the digital=20 mixing maximum of 0dBFS. (We=EF=BF=BDll explain the = =EF=BF=BDdBFS=EF=BF=BD part in a=20 moment, but at this point it=EF=BF=BDs worthwhile to = note that to=20 avoid the clipping problem at this point you should = either be=20 reducing the output bus level by 0dB, or reducing all = of the=20 10 tracks feeding the Output Bus by 10dB apiece, which = has the=20 same effect.)

Ramifications For Digital=20 Audio

Remember how I said that cloning an = instrument=20 (thereby doubling its intensity, or sound pressure) = raises=20 things by 6.02dB? Well, we like to double things in = the=20 digital world; it happens every time we add an extra = bit of=20 precision. How many times have you bought a CD and = read the=20 little liner note thingy explaining how great = CD=EF=BF=BDs are? (=EF=BF=BDThe=20 high resolution of this Compact disc may reveal = limitations in=20 the master tape, including noise and other = distortions.=EF=BF=BD)=20 Well, that=EF=BF=BDs because being 16-bit, Compact = discs have a=20 dynamic range of 16*6.02dB =3D 96.32dBFS which is well = beyond=20 the 60 dB or so of dynamic range that LP records were = capable=20 of. Dynamic Range is the difference between the = loudest sound=20 playable to the softest, and for anybody who caught my = =EF=BF=BDPreserve Your Bits=EF=BF=BD article on Guitar = School that=EF=BF=BDs 65,536=20 times louder. So is this enough? Most certainly not; = the ear=20 has a good 120dB dynamic range (up to the = =EF=BF=BDthreshold of pain=EF=BF=BD)=20 so while the dynamic range of the compact disc is not = perfect,=20 CD=EF=BF=BDs are much better than any consumer format = we had=20 prior.

So what kind of wordlength should = CD=EF=BF=BDs have been=20 given in order to supply to 120dB=EF=BF=BD worth of = dynamic range? The=20 answer is  120dB / 6.02dB, or 19.93 bits. Looks = like=20 those 20-bit ADAT decks from the 90=EF=BF=BDs were = good enough! That=EF=BF=BDs=20 not something that consumers ever saw, however the = 24-bit=20 consumer =EF=BF=BDaudiophile=EF=BF=BD standard today = is better still (and more=20 than good enough.) In the old days those = =EF=BF=BDlimitations in the=20 master tape and other distortions=EF=BF=BD were always = there =EF=BF=BD we just=20 couldn=EF=BF=BDt hear them, because they were lost = among all the noise=20 and turntable rumble!

=EF=BF=BDSPL=EF=BF=BD and = =EF=BF=BDdBFS=EF=BF=BD Explained, Along=20 With All The Rest

Up until this point, = we=EF=BF=BDve avoided=20 giving a formal definition of what a decibel is. This = is where=20 I=EF=BF=BDm going to step aside and let Ken = Pohlmann=EF=BF=BDs classic=20 =EF=BF=BDPrinciples Of Digital Audio (5th ed.) do it = for=20 me:

Specifically, the decibel is defined to be = 10 times=20 the logarithm of a power ratio:

Intensity level = =3D 10=20 log(P1/P2) dB

where P1 and P2 are values of = acoustical=20 or electrical power.

If the denominator is set = to a=20 reference value, standard measurements can be made. In = acoustic measurements, an intensity level (IL) can be = measured=20 in decibels by setting the reference intensity to the=20 threshold of hearing, which is 10^-12 W/m^2 (watts per = square=20 meter). Thus the intensity level of a rock band = producing=20 sound power of 10W/m^2 can be = calculated:

Intensity=20 level =3D 10 log(P1/P2) dB =3D 10 log(10^1/10^-12) =3D = 130dB=20 SPL

Going in the reverse (antilog) direction is = trivial:

Sound Pressure Ratio =3D antilog(130dB = SPL/10) =3D=20 10^(130/10) =3D 10,000,000,000,000 (x 0dB = SPL)

Note that=20 when ratios of currents, voltages or sound pressures = are used=20 (quantities whose square is proportional to power), = the above=20 decibel formulas must be multiplied by = 2.

(DJ=EF=BF=BDs Math=20 Refresher: The (base-10) log of a number is simply the = number=20 you=EF=BF=BDd have to raise 10 to the power of in = order to get the=20 desired number. In other words, the log of 1000 (i.e., = 10^3)=20 is 3. The Antilog of 3 is 10^3, or 1000. It helps to = open up=20 the Windows Calculator in Scientific Mode and play = around with=20 these formulas a bit until they feel = comfortable.)

I=20 know I=EF=BF=BDve probably lost everybody at this = point, but what Ken=20 is trying to say is that dB=EF=BF=BDs don=EF=BF=BDt = exist in a vacuum; they=EF=BF=BDre=20 always relative to something and that relationship is = always=20 expressed as a ratio of powers. What is power? In = physics,=20 Power is the ability to do Work. And what is work? = Imagine a=20 river that feeds a hydroelectric plant, like Niagra = Falls.=20 What kind of river can generate the most electricity = (work)?=20 One that has a lot of water (current) moving at a high = rate of=20 speed (pressure). Multiplying these two figures gives = you the=20 river=EF=BF=BDs power, which might be expressed in = terms of something=20 like gallons per minute (GPM). In electricity, the = analogy is=20 the same, only Power is expressed in Watts, and Watts = =3D=20 current (there=EF=BF=BDs that word again) * voltage=20 (pressure).

When the Bel scale was invented it = was=20 originally used for measuring signal power loss over = telephone=20 lines, hence its standardization around = =EF=BF=BDpower=EF=BF=BD measurements.=20 Much of the audio world, however, involves measuring = pressure=20 or intensity, not power. However, power is = proportional to=20 intensity, and you can perform =EF=BF=BDpressure to = power=EF=BF=BD conversions=20 on the fly simply by squaring the pressure. (To = understand=20 this fully, consider that in Ohm=EF=BF=BDs Law, in a = circuit with a=20 resistance of 1 ohm voltage and current are always = identical =EF=BF=BD=20 and therefore, the formula of Watts (power) =3D Volts = * Amps is=20 equivalent to Volts or Amps squared.) Incidentally, a = deciBel=20 is simply a Bel measurement multiplied by 10, which = figures=20 into the formulas above and below. This gives us an = extra=20 digit of precision when quoting measurements, as = saying things=20 like =EF=BF=BDthe human ear has 12.0 Bel of dynamic = range=EF=BF=BD seemed a=20 little too coarse back when the scale was = invented.

So=20 when computing dB values based on pressure or = intensity,=20 (which would include almost everything that = wasn=EF=BF=BDt a Watt or=20 pre-squared in some other fashion) the decibel formula = needs=20 to be written like so:

Intensity level =3D 20=20 log(p1/p2)dB

where p1 and p2 are values of = acoustical=20 of electrical pressure. (Changing the = =EF=BF=BD10=EF=BF=BD to =EF=BF=BD20=EF=BF=BD before the=20 log is equivalent to squaring p1 and p2 in the formula = above,=20 only easier =EF=BF=BD such is the power of = logarithms.)

In this=20 example, we=EF=BF=BDll compute the maximum dBFS = (FS=3DFull Scale) of a=20 16-bit word as used in a compact disc. The maximum = value would=20 be 65536, and the minimum value would be one. The = dynamic=20 range of a compact disc is, = therefore:

Intensity level=20 =3D 20 log(p1/p2) dB =3D 20 log(65536/1) =3D ~96.32=20 dBFS

Going in the reverse (antilog) direction = is even=20 easier:

16-Bits Full Scale =3D antilog(96.32 = dbFS/20) =3D=20 10^(96.32/20) =3D ~65,536 (x 1)


Doing = Decibels In=20 Your Head (taken from Dave Moulton=EF=BF=BDs = =EF=BF=BDTotal=20 Recording=EF=BF=BD)

Doing all this in your head = is fairly easy,=20 believe it or not. Keep in mind the following basic=20 equivalents:

FOR POWER FOR PRESSURE
3 dB =3D = 2 x power=20 6 dB =3D 2 x pressure
-3dB =3D .5 x power -6 dB =3D = .5 x=20 pressure
6 dB =3D 4 x power 10 dB =3D 3.16 x = pressure
-6 dB=20 =3D .25 x power -10dB =3D .316 x pressure
7 dB =3D = 5 x power 12=20 dB =3D 4 x pressure
9 dB =3D 8 x power -12 dB =3D = .25 x=20 pressure
10 dB =3D 10 x power 14 dB =3D 5 x = pressure
-20 dB=20 =3D .01 x power 18 dB =3D 8 x pressure
13 dB =3D 20 = x power 20 dB=20 =3D 10 x pressure
17 dB =3D 50 x power -40dB =3D = .01 x=20 pressure
20 dB =3D 100 x power 26 dB =3D 40 x = pressure
30 dB=20 =3D 1,000 x power, etc. 34 dB =3D 50 x pressure
40 = dB =3D 100 x=20 pressure
60 dB =3D 1,000 x pressure, = etc.

Using these,=20 you can work out just about anything you want. For = instance,=20 33dB is a power ratio of 2000 (3 dB over 1000), or a = pressure=20 ratio of a little less than 50. A little practice and = you=EF=BF=BDll=20 have it in no time.

Decibel References (also = taken from=20 Dave Moulton=EF=BF=BDs =EF=BF=BDTotal = Recording=EF=BF=BD)

As I=EF=BF=BDve mentioned,=20 decibels are simply alternative numbers that represent = ratios=20 of power (and, indirectly, pressure). Naturally, there = are=20 many occasions when we want to know the ratio, = expressed in=20 decibels, between some value and a known, standardized = reference. As a result of this need, an array of = decibel=20 references have evolved over the years. Below are = several such=20 references that are in common use today for audio, = along with=20 some discussion of their applications.

0 dB SPL = =3D .0002=20 microbars =3D .0002 dynes/cm^2 =3D .00002 = Pascals
This=20 reference is for the threshold of hearing. It is an = acoustic=20 expression of pressure (all calculations should use = the=20 pressure multiplier, 20) that represents the pressure = level of=20 the softest 1KHz sound that average humans can detect. = Any=20 expression of acoustical amplitude using dB is usually = derived=20 from this value.

0 dbW =3D 1 Watt
This = reference is a=20 power reference tied to Watts, generally used with = power=20 amplifiers.

0dBM =3D 1 milliWatt
This = reference has=20 become a little ambiguous. In its original form, it=20 unequivocally referred to 1 milliWatt of power, for = use in=20 telephone and other audio transmission = lines.

At that=20 time, power management was a critical issue, and so=20 transmission systems used matched impedance systems = for the=20 most efficient transfer of power between elements in a = system.=20 In telephone practice, the standard source and input = impedance=20 of all devices was 600 ohms. Given that impedance, the = voltage=20 level needed to generate 1 milliWatt of power is .775 = volts.=20 As a result, 0 dBM has, over the years, come to refer=20 informally to .775 volts in common practice, = regardless of the=20 load. (If the load is not 600 ohms, then .775 volts = will not=20 generate 1 milliWatt of power.)

So, the literal = usage=20 of 0dbM is as a power reference of 1 milliWatt, while = the=20 sloppier common-practice usage is as a voltage = reference of=20 .775 volts. When you run across the dBM reference in = specs and=20 advertising for modern audio gear, it almost always is = the=20 common-practive reference. We simply aren=EF=BF=BDt = concerned about=20 the power issue at line levels anymore.

For the = more=20 literal-minded and anal-retentive among us, there is a = more=20 formal voltage reference to use:

0 dBu =3D .775 = Volts
This reference is unequivocal. It is the = voltage=20 reference that is equivalent to 0dBM when a 600-ohm = load is=20 present. It is a standard audio reference. = (Dallas=EF=BF=BD note:=20 +4dbU (1.23V) is the standard signal level for = balanced=20 professional audio gear)

0dBV =3D 1 = Volt
This=20 reference is an obvious and convenient one. It is = unfortunate=20 that it is only 2.2 dB from 0dBu,which causes the two = to get=20 tangled up a lot. The confusion is magnified by the = casual=20 practice of some engineers to refer to 1 Volt with a = capital=20 =EF=BF=BDV=EF=BF=BD and to .775 volts with a = lower-case =EF=BF=BDv=EF=BF=BD. So, the bad news=20 is that this particular specification is a bit of a = minefield,=20 and you=EF=BF=BDve got to proceed with a little = caution. The good news=20 is that if you get it wrong, you=EF=BF=BDre only off = by 2dB!

If=20 I were king, I=EF=BF=BDd abolish the .775 volt = reference now, and have=20 a single line-level voltage of 0 dBV =3D 1 Volt. = (Dallas=EF=BF=BDs note:=20 -10dbV (3.16V) is the standard signal level for = unbalanced=20 consumer audio gear)

0 dBFS =3D Digital Audio = Level at=20 the top of the  Most Significant Bit
dBFS = (Full Scale)=20 is a digital audio reference. It equals the maximum = level on a=20 meter used to measure a digital audio sine wave = signal, and=20 typically in digital audio, it refers to the level of = a sine=20 wave at the top of all bits, or the maximum capacity = of the=20 digital word used to represent the audio information. = The=20 practical consequence of this is that 0 dBFS = represents the=20 peak level the system can handle without=20 overloading.

There are numerous other decibel=20 references. The principle is the same: a symbol = following the=20 term dB refers to some standard value that will be 0dB = for=20 that reference system. All you=EF=BF=BDve got to do is = find out what=20 the reference is!

Actually, you can even have = fun with=20 this and make up your own decibel references. For = instance, as=20 a teaching example I created the Nugent, or dBN, where = 0dbN =3D=20 the sound pressure level of Ted Nugent playing a power = chord=20 at full level. Question: How many Ted Nugents playing = a single=20 power chord all at once does it take to generate a = sound=20 pressure level of 40 dbN? Answer, 10,000! It=EF=BF=BDs = enough to make=20 you think carefully about this = business!

Finally, as=20 you work with decibels, you=EF=BF=BDve got to stay = aware of exactly=20 when you=EF=BF=BDre working with decibels as ratios = and when as=20 decibel references. Any decibel value tied to a = reference=20 (say, -21 dBu) is a fixed value, while 21dB is just a = ratio.=20 If, for example, you say, =EF=BF=BDI=EF=BF=BDd like a = 3dB pay increase,=EF=BF=BD you=20 are saying you=EF=BF=BDd like to double your salary! = This is quite a=20 bit different than saying =EF=BF=BDI=EF=BF=BDd like to = earn 3=20 dB$.=EF=BF=BD

(dB$ is an obscure capitalist = reference, where=20 0dB$ =3D $1. In the example, you are asking for=20 $2!)


Dallas=EF=BF=BD Wrap = Up

That=EF=BF=BDs it for this=20 tutorial, and believe me it was a very difficult one = to write.=20 Decibels were on my mind this week and there=EF=BF=BDs = no better way=20 to test one=EF=BF=BDs degree of understanding in a = concept then by=20 trying to explain it to someone else. For more info, = (a lot=20 more) check out David Moulton=EF=BF=BDs =EF=BF=BDTotal = Recording=EF=BF=BD and Ken=20 Pohlmann=EF=BF=BDs =EF=BF=BDPrinciples Of Digital = Audio=EF=BF=BD, now in its fifth=20 edition. This little write-up represents what I find = most=20 useful in thinking about dB=EF=BF=BDs, and as wordy as = it is I felt=20 like I couldn=EF=BF=BDt make it any shorter with = leaving something=20 important out!

Happy = recording,

-djh

4 comment(s) | viewed = 97 time(s)=20 | 3Dprint=20 |

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Commented by CapnZilog - Oct 29, 2006 = @=20 04:28:05 AM
OK, now that the = School's PHP is=20 working again, let's try a second time posting this = one. I=20 gave up trying to make the HTML formatting work = properly here=20 though, as there's too much HTML munging going on = behind the=20 scenes. Maybe in the future we'll be allowed to post = PDF's=20 instead?
Commented by CapnZilog - Dec 20, 2006 = @=20 06:17:00 PM
Version 1.3 up at=20 http://dallashodgson.info/files/DecibelPrimer.pdf, = correcting=20 a bug in the "130dB rock band" SPL formula=20 example
Commented by CIRCLEjerk - Jan 03, 2007 = @=20 08:57:52 PM  
that was extremely = interesting...i=20 really liked the part on the ramifications of a = compact=20 disk...i need to brush up on my learnin' as far as = that stuff=20 goes.
Commented by GtrZan - Jan 31, 2007 @ = 11:11:02=20 AM  
That ws great = Dallas!

Being=20 an RF engineer I LIVE in the world of dB (dBm, to be = more=20 precise). This presents the entire concept including = the=20 history of the scale very=20 succinctly.

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=20

= =20


v2.0 = 2001-2004

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