Odd statement in Audacity manual

[Timar]

Hi there,

when reading through the Audacity manual I stumbled over the following statement which seems quite irritating to me:

the dynamic range on an audio CD is theoretically about 90 dB, but realistically signals that are -24 dB or more in volume are greatly reduced in quality

http://audacityteam.org/manual-1.2/tuto ... ics_1.html

I wonder what scientific knowledge this assertion is based upon? First, the dynamic range of an audio CD is not "about 90" but quite exactly 96dB (psychoacoustical effects of dithering left aside). Second, for what reason should signals <= -24 dB FS become "greatly reduced in quality"? I just don't see it...

Sorry to be nitpicking here, but when it comes to bitdepth there seems to be much confusion - many people who firmly believe that 16bit as an distribution format would sound inferior to 24bit or DSD, without knowing anything about digital audio. A stetement like this could adds only to that kind of confusion...

[waxcylinder]

You have posted in the 1.3 section of the Forum, so I'm puzzled why you are reading the now ancient 1.2 manual.

The 1.3 manual can be read here: http://manual.audacityteam.org/man/Main_Page

This is what the 1.3 manual cuuremly says on CDs: http://manual.audacityteam.org/man/Audio_CDs
And this is the page on Digital Audio: http://manual.audacityteam.org/man/Digital_Audio
Care to comment on those for us? And then we can consider amendments.

WC

[waxcylinder]

I note that Wikipedia page: http://en.wikipedia.org/wiki/Dynamic_range

States (my bolding):
The 16-bit compact disc has a theoretical dynamic range of about 96 dB[7] (or about 98 dB for sinusoidal signals, per the formula[6]). Digital audio with 20-bit digitization is theoretically capable of 120 dB dynamic range; similarly, 24-bit digital audio calculates to 144 dB dynamic range.[4] All digital audio recording and playback chains include input and output converters and associated analog circuitry, significantly limiting practical dynamic range. Observed 16-bit digital audio dynamic range is about 90 dB.[7]

So I'm guessing that the manual page was written with practicality rather than theory in mind. Any thoughts?

WC

[steve]

the dynamic range on an audio CD is theoretically about 90 dB, but realistically signals that are -24 dB or more in volume are greatly reduced in quality

I don't see it either. IMO that's either wrong, or written so badly as to be misleading.

[Timar]

You have posted in the 1.3 section of the Forum, so I'm puzzled why you are reading the now ancient 1.2 manual.

The 1.3 manual can be read here: http://manual.audacityteam.org/man/Main_Page

This is what the 1.3 manual cuuremly says on CDs: http://manual.audacityteam.org/man/Audio_CDs
And this is the page on Digital Audio: http://manual.audacityteam.org/man/Digital_Audio
Care to comment on those for us? And then we can consider amendments.

WC

I didn't post it on the 1.2 forum because it is closed But I didn't know that there is an updated manual for 1.3. Looks much better indeed, the misleading statement is gone. However, there are a few point which could be clarified even further (from the Digital Audio Page):

Therefore a sample rate of 40,000 Hz is the absolute minimum necessary to reproduce sounds within the range of human hearing, though higher rates (called over sampling) may increase quality even further by avoiding any aliasing artifacts around the Nyquist frequency. The sample rate used by audio CDs is 44100 Hz

This could give the wrong impression that higher sample rates than 40kHz (or 44.1?) are generally called "over sampling", though the term only applies if the sampling rate is multiplied by a natural number n, thereby interpolating between the original samples. Yep, this may avoid aliasing when using inferior D/A converters (almost any recent converter does 4x-128x oversampling internally), or when doing nonlinear processing which could generate HF content above the Nyquist frequency. But of course, when you have PCM material which has a native sampling frequency of 96kHz or more, it isn't oversampled!

States (my bolding):
The 16-bit compact disc has a theoretical dynamic range of about 96 dB[7] (or about 98 dB for sinusoidal signals, per the formula[6]). Digital audio with 20-bit digitization is theoretically capable of 120 dB dynamic range; similarly, 24-bit digital audio calculates to 144 dB dynamic range.[4] All digital audio recording and playback chains include input and output converters and associated analog circuitry, significantly limiting practical dynamic range. Observed 16-bit digital audio dynamic range is about 90 dB.[7]

Well, the dynamic range 16bit PCM can possibly hold is about 96dB, that's it. If "oberserved dynamic" range is below that value, it is because there are not many analogue components which can record or reproduce such an dynamic range. Another point is that the recorded material hardly ever has a dynamic range above 50dB, even for very dynamic orchestral music. If one would look at recent rock CDs the "observed" dynamic range would probably be around 10dB (loudness wars rulez)!

But this figure hasn't anything to do with the technical limitations of the 16bit format! It's quite the same situation for 24 or even 32 bit audio. That's why this list is still mysterious:

Common sample formats, and their respective dynamic range include:

8-bit integer: 45 dB
16-bit integer: 90 dB
24-bit integer: 135 dB
32-bit floating point: near-infinite dB

The quoted value seem to be made up of thin air. I have no idea where they come from. As this page is a technical explanation I really think one should stick to the technical specifications and name the actual dynamic range a bit depth can hold. And that's 1.76+6.02n, commonly rounded to 6n.

[steve]

I didn't post it on the 1.2 forum because it is closed

All development of the 1.2 series of Audacity ended some years ago. The Audacity 1.2 "General Feedback and Discussion" board was closed as it seems fairly pointless to gather feedback about Audacity 1.2, given that no changes will be made to that version. We don't have a forum board about documentation, so I guess this board is as good as any for this discussion.

This could give the wrong impression that higher sample rates than 40kHz (or 44.1?) are generally called "over sampling",

Oversampling is defined on Wikipedia as "In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled." http://en.wikipedia.org/wiki/Oversampling
This is a more general (but accurate) definition than the specific case of Oversampling DACs.
As the audio bandwidth is 20 Hz - 20 kHz, a sampling frequency of 96 kHz is oversampling, (regardless of whether or not an oversampling DAC is being used).

The quoted value seem to be made up of thin air. I have no idea where they come from. As this page is a technical explanation I really think one should stick to the technical specifications and name the actual dynamic range a bit depth can hold.

I agree that the quoted dynamic ranges look odd.

I would prefer:
8-bit integer: 48 dB
16-bit integer: 96 dB
24-bit integer: 144 dB
32-bit floating point: around 1500 dB

This is not quite accurate on a couple of counts. 1) because (as you say) "x 6" is only an approximation 2) With correct dithering the signal level can be substantially lower than the RMS noise floor. However, these are the most commonly quoted figures and the "x 6" calculation is a reasonable (if slightly over simplified) basis for the figures.

[Timar]

This could give the wrong impression that higher sample rates than 40kHz (or 44.1?) are generally called "over sampling",

Oversampling is defined on Wikipedia as "In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled." http://en.wikipedia.org/wiki/Oversampling
This is a more general (but accurate) definition than the specific case of Oversampling DACs.
As the audio bandwidth is 20 Hz - 20 kHz, a sampling frequency of 96 kHz is oversampling, (regardless of whether or not an oversampling DAC is being used).

That's true, but is is only slighly more general than the definition given by me. Even if in therory the oversampling factor doesn't necessarily have to be a natural number (but for practical reasons always is), we are still considering a sampling frequency "significantly higher" than the Nyquist frequency for the highest signal content. This definition is obviously not true for a native 96khz signal containing frequency content up to 48kHz, regardless of anyone beeing able to hear that stuff. I'm just saying that that oversampling is something different than having a native frequency of more than 44.1khz and that this difference should be made clear.

I would prefer:
8-bit integer: 48 dB
16-bit integer: 96 dB
24-bit integer: 144 dB
32-bit floating point: around 1500 dB

This is not quite accurate on a couple of counts. 1) because (as you say) "x 6" is only an approximation 2) With correct dithering the signal level can be substantially lower than the RMS noise floor. However, these are the most commonly quoted figures and the "x 6" calculation is a reasonable (if slightly over simplified) basis for the figures.

Agreed. It is not quite accurate of course, but from a technical perspective it is far more accurate than the odd values we have now. I'd say it's ok not to mention dithering at this place because 1) it would complicate things unneccesarrily and 2) it's not strictly a physical but rather a psychoaccoustical effect.

[Gale Andrews]

This could give the wrong impression that higher sample rates than 40kHz (or 44.1?) are generally called "over sampling",

Oversampling is defined on Wikipedia as "In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled." http://en.wikipedia.org/wiki/Oversampling
This is a more general (but accurate) definition than the specific case of Oversampling DACs.
As the audio bandwidth is 20 Hz - 20 kHz, a sampling frequency of 96 kHz is oversampling, (regardless of whether or not an oversampling DAC is being used).

That's true, but is is only slighly more general than the definition given by me. Even if in therory the oversampling factor doesn't necessarily have to be a natural number (but for practical reasons always is), we are still considering a sampling frequency "significantly higher" than the Nyquist frequency for the highest signal content. This definition is obviously not true for a native 96khz signal containing frequency content up to 48kHz, regardless of anyone beeing able to hear that stuff. I'm just saying that that oversampling is something different than having a native frequency of more than 44.1khz and that this difference should be made clear.

I agree it would be better to make it clearer for those who don't click the Wiki link, but I think it would mean extra text - my suggestion:

Code: Select all

Therefore a sample rate of 40000 Hz is the absolute minimum necessary to reproduce sounds within the range of human hearing. However using 40000 Hz as a sample rate would risk audible aliasing artifacts around the Nyquist frequency, so a sample rate of 44100 Hz was chosen as the standard for audio CDs. Using a sample rate significantly in excess of twice the bandwidth to avoid artifacts is known as oversampling.

I would prefer:
8-bit integer: 48 dB
16-bit integer: 96 dB
24-bit integer: 144 dB
32-bit floating point: around 1500 dB

This is not quite accurate on a couple of counts. 1) because (as you say) "x 6" is only an approximation 2) With correct dithering the signal level can be substantially lower than the RMS noise floor. However, these are the most commonly quoted figures and the "x 6" calculation is a reasonable (if slightly over simplified) basis for the figures.

I've changed the Manual to use the values given in the Audacity Interface Preferences:

8-bit integer: 48 dB
16-bit integer: 96 dB
24-bit integer: 145 dB

Conversations on audacity-devel and elsewhere frequently refer to the "near-infinite" dynamic range of 32-bit float, so I haven't changed that in the Manual (yet). Where is the difference arising between 1500 dB and "near-infinite"? "Near-infinite" gets mentioned in terms of amplification edits in 32-bit float never causing loss of dynamic range.

the dynamic range on an audio CD is theoretically about 90 dB, but realistically signals that are -24 dB or more in volume are greatly reduced in quality

If we can agree what to change it to, I'll change that. "Theoretically 96 dB" is a simple change. Clearly digital quality does fall off with reduced level but I don't know where the -24 dB threshold comes from. Perhaps it should be saying there is a practical limit of -90 dB and that signals at low levels have lower fidelity because they do not use all the available bit depth?



Gale

[steve]

This definition is obviously not true for a native 96khz signal containing frequency content up to 48kHz,

48 kHz is "inaudible" - that is, "not audio".
Regardless of the supported sample rates, good quality sound cards will limit the bandwidth to around 22 kHz (so as to fully encompass the full audio spectrum, but avoid unnecessary high frequency interference). According to the Nyquist–Shannon sampling theorem, the required sample rate for representing a 22 kHz bandwidth is 44 kHz. Significantly greater than that is "over" sampling.
This is obviously not true for scientific AD converters that may have a much greater bandwidth than the audio frequency range.

Where is the difference arising between 1500 dB and "near-infinite"?

1500 dB is virtually insignificant compared with 10^1000000000 dB, but even that figure is infinitely smaller than "infinite" dB, but this is probably just me being pedantic "Near infinite" is probably good enough to get across the idea of "absolutely enormous" dynamic range.