Bit-resolution and Clipping?

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Can a wave file with stronger bit-resolution handle more decibels
w/out clipping than a wave file with weaker bit-resolution?

 

Can a wave file with stronger bit-resolution handle more decibels

Yes. The dynamic range is proportional to the number of bits,
assuming that you're talking about linear PCM. The dynamic range is
approximately 6 dB per bit.

So, with more bits, you can handle larger signals at the "loud" end
(without clipping) or smaller details at the "quiet end" (without
losing them below the quantization-noise floor), or both. It all
depends what signal levels you choose to treat as "full scale" and
"least significant bit".

 

So a digital audio device with a bit-resolution of 100-bit can handle
up to 600 dB w/out clipping. Right?

 

The dynamic range is

In theory, yes, in the absence of noise and other dynamic range limits.

In practice, it's useless to try. Even 32 bits is more than you can
usefully expect to represent within reasonable physical limits. I
think I recall reading an analysis a few years ago (JJ's, perhaps?)
which pointed out that if you try to use a 32-bit linear PCM system,
and set the least significant bit down to somewhat below the human
ear's ability to hear any sound in a perfectly quiet room, then a
full-scale 32-bit CD-quality signal would release so much energy that
it would vaporize the listening equipment (and probably the listener,
too).

Doesn't make for a relaxing evening... a log in the fireplace, a nice
glass of wine, and a pleasant CD on the
BWOOM!

 

Only if the analogue gear it's attached to can cope with this range!

 

OOOOOOOOOPS!!!!!

I forgot to add that this theoretical digital audio device also
contain a 100-bit DAC. Sorry.

 

Which will of course have an output dynamic range of less than 22
bits, as with all available '24 bit' DACs...................

 

You mean the DAC?

 

Speaking of digital vs. analog, analog clipping isn't as harsh as
digital clipping. However, CDs have a dynamic range of approx. 90dB
and tapes have it at about 60dB. This means a CD can handle 90 dB
w/out clipping, while a tape can only handle 60dB. Right?

 

Why?

 

Which will of course have an output dynamic range of less than 22

Several reasons. Noise is one.

All electronics generate noise. One type, known as "thermal" noise,
occurs any time you have a resistance - the amount of noise depends on
the resistance and the temperature. If you set the maximum output
voltage of your DAC to a useful standard level (e.g. 2 volts
peak-to-peak, as is fairly usual for CD players and other line-level
outputs), you'll find that the thermal noise generated by the
resistances in the DAC circuitry will be down in the 24-bit region.
If you try to resolve signals smaller than that, they'll be buried in
the noise.

You can try cooling the DAC down with liquid nitrogen, and maybe
that'll get you another bit or two in noise performance, but it's
going to be expensive in the long run.

Linearity is also an issue. In order to reproduce very-low-level
signals with a DAC, the DAC's internal electronics must be very, very,
VERY accurate... and at some point, the necessary accuracy moves
past the "expensive" point, to "beyond the state of the manufacturing
art" Twilight Zone.

 

Well, now, think about it. What do YOU think 600 dB means?

Well, if you haven't gotten there, 600 dB means there is a factor
of 1,000,000,000,000,000,000,000,000,000,000 between the amplitudes
of the smallest and largest representable signals. That's 10^30
power.

Fine, so figure out what THAT means.

Okay, didn't bother to go there yet? Fine.

Let's look at hooking up a h-fi system to this rather silly device.
Let's assume that you have adjusted the volume control so that the
very smallest signal this device can put out generates a sound that
is 1/100 as loud as the faintest signal you can hear, that is, at
a sound pressure level of -20 dB re 10^12 watt/m^2 (that's a trillionth
of a watt per square meter).

Fine. How loud can it play? Well, according to you, 600 dB -20 dB or
580 dB SPL. Great, what does THAT mean?

Well, if it's 580 dB above 1 trillionth of a watt, that's 10^27 watts
per square meter of acoustical power. Let's just, for the sake of
simplicity, assume the entire acoustical radiation is confined to that
1 square meter The amount of acoustic power you want to put into that
small area is something like 1,000,000,000,000,000 times greater then
the entire amount of electrical power consumed by the entire United
States for all conceivable and inconceivable reasons. And let's assume that
your speakers are pretty efficienct, say 10%. That means you are going
to have to find yourself an amplifier capable of putting out somewhere
in the range of 10,000,000,000,000,000 watts. Assume such an amplifier
is running at about 40% efficiency. How much power would you need?

Well, the entire output energy output of the sun is probably insufficient
to the task.

Got it?

 

What are you trying to achieve, Mr Radium? Will you put out question
after question until you feel educated?

Methinks Radium is a troll. Nobody can be this stupid, based on the
the questions asked so far.

But it *is* fun when D. Pierce does his usual
you-asked-for-the-reason-here-it-comes computing of needed power!

I can see the ad in front of me: "The new Gizmo 600dB amp will
outperform the sun!"

Per.

 

And the microphones............

 

It can be - that's too sweeping a generalisation.

Correct.

 

Because of the dynamic range of the analogue output stage.

 

Because of the dynamic range of the analogue output stage. The
standard full-scale output level is 2 volts rms, and the self-noise of
most line stages is seldom less than 2 microvolts. This is a 120dB
dynamic range, or 20 bits.

Check out the specs of most '24-bit' DACs, and you'll very seldom see
dynamic range quoted at more than 114 dB, which is only 19 bits. I
believe that the current state of the art is represented by the dCS
and Apogee professional converters, which run out around 125dB, just
under 21 bits.

Of course, bearing in mind that no music master tape in the history of
the world has ever exceeded a dynamic range of 85dB, and that hardly
any studio microphones have a DR of more than 100dB, you'll see that
this in't a problem in the real world!

 

Perhaps a simpler analogy would be that it represents rather more than
the dynamic range that you would experience if you were standing in
the New Mexico desert at midnight on a perfectly still night - and a
cruise missile exploded ten feet away...........

 

The multimedia speakers for PC's will get there first .... it was indeed
a well written and entertaining discourse Mr. Pierce delivered.

Seasons Greetings / God Jul

Peter Larsen

 

Not true. Both analog and digital circuits can put very nice flat tops on
your music waveforms.

Right. In practice this means that you can allow more headroom without
getting fried by hiss at low levels.