Bit depth revisited - Page 5

chris319 · 14th April 2009

Quote:

"If the 16-bit ruler measured 100 cm (or 1000 mm) the 24 bit one should measure 150 cm (or 1500 mm)."

This is where you go fundamentally wrong... Both are of equal length

You need to put this in the context of the analog noise floor being about -120 dBFS (using round numbers). That is the limiting factor. It is easy to see that a device which only resolves down to -96 dBFS can't resolve information below that (the -120 dBFS analog noise floor). That's the "short ruler" part of the analogy". A device which can resolve down to -144 dBFS can. That's the "long ruler" part of the analogy.

chris319 · 14th April 2009

Quote:

Originally Posted by David Rick

Audio is converted as linear PCM, which means that adjacent codes represent equal steps in voltage or pressure, not equal steps in dB.

No. The steps are finer in the 24 bit case. This is true over the full range. I already posted the math in an earlier response.

Yes, I can do the math.

David L. Rick

Here's the (simplified) math again for those of you who missed it:

Quote:

A standard audio ADC requires 2V peak to peak to light up all the bits. With 16 bits you can resolve down to .0305 mV. In much of today's electronic circuitry the noise floor is down around .0019 mV. Thus, the first step of a 16-bit system cannot resolve all the way down to noise-floor voltages. Compare that to our 24-bit system which can resolve well into the noise floor, as low as .00012 mV.

The principles are the same whether you measure in volts or decibels:

16 bits = .0305 mV = -96 dBFS = lowest resolvable signal component

20 bits = .0019 mV = -120 dBFS = noise floor of modern analog circuitry

24 bits = .00012 mV = -144 dBFS = lowest resolvable signal component

d_fu · 14th April 2009

Quote:

Originally Posted by Nishmaster

It is not more "accurate" in the sense of the word, which is the misconception that gets tossed around most often.

I would say the term does apply WRT to the finer "steps", i.e. changes of amplitude will be sampled/digitized more accurately or more precisely. 24 bit sampling does not provide greater accuracy WRT to the sampled waveform's phase (position), though.

Audiop · 14th April 2009

Quote:

Originally Posted by klaukholm

Guys, everybody is arguing about two related issues. If you can answer it simply with reliable math, I will go away.

1. Is PCM sampling amplitude in equal divisions of dB steps or some other division?

2. Do 24 bit and 16bit capture amplitute with the same divisions down to -96?

PCM is working on the basis of binary numbers. A 3bit wordlength can have the following combinations: 000 - 100 - 010 - 110 - 001 - 101 - 011 - 111 and can therefore represent eight different values from zero (000) to seven (111). We can give the first position the value of 1, the second position the value of 2 and the third position the value of 4.

The 3bit wordlength for a given voltage representing 0dBFS will give 1/7 of full scale on each step and a dynamic range of 18dB

If we increase the wordlength to 4bit we can have the following combinations: 0000 - 1000 - 0100 - 1100 - 0010 - 1010 - 0110- 1110 - 0001 - 1001 - 0101 - 1101 - 0011 - 1011 - 0111 - 1111. The 4bit combinations give us sixteen different values from zero to fifteen. Here we build upon the first 3bit series and the rightmost(?) position have the value 8. For the same voltage as the 3bit example representing 0dBFS we have higher resolution (= lower noise) since each step is 1/15. The 4bit wordlength give us 24dB dynamic range, an increase of 6dB/1bit from the first example with 3bit.

Confessiontime:

I don't know if I have the details correct here but this is my simplified understanding and I do think it serves the purpose of giving a basic view of the subject.

If the signal is static/periodic like music is partly we will have correlation of the quantization steps and that means distortion plus correlated/signal dependent noise. If the signal has non static/periodic content (noise) continously that is higher in level than the quantization steps this will decorrelate the quantization distortion and turn it into noise. In 24bit audio we dont have to add dither since first of all, the quantization errors are so small and also because the analog noise from all earlier stages will serve as dither noise.

In 16bit audio the analog noise may be lower than the quantization steps and therefore we may need to add dither noise in order to decorrelate the quantization errors.

The general view of those that have a grip on this (the way I understand) is that if the noise from the digital system is inaudible, then that resolution is all you need and that means that for many situations 16bit audio can't be bettered by higher resolution by longer wordlength.

/Peter

Ozpeter · 15th April 2009

Quote:

it is not "demonstrably reproduced only at levels 96dB below full scale". maybe go record some real music, with a properly calibrated sampler, at a good level, and see.

and maybe use a real daw.

There is simply no room for doubt on this. It is not an opinion, it is a fact that anyone here can determine for themselves using their own system. If you have not bothered to do that, and you doubt the validity of my test, repeat it yourself using any 24 bit file, and you will come up with the same result. And any DAW will do the job, unless it has gross errors in its code.

If one examines the difference file at considerable zoom levels (don't try that using the mp3 version I posted though - the mp3 encoding stuffs the detail), it's what you would expect to see if one follows Nishmaster's explanation - you see the quantisation error signal having exactly the visual character of Nishmaster's very handy illustration where the original audio has samples above 96dB below full scale, and where the audio is entirely below 96dB below full scale, it's the normal-looking waveform representing that audio. And as all values in that difference file have had the first 16 bits set to zero by the process of obtaining the difference by inversion, the reproduced level is bound to peak no higher than 96dB below full scale (or thereabouts).

It's also uncontestably true that if you mix (add) that very low level 24-bit difference file to the 16 bit file truncated from the original, you get the original 24 bit recording back, bit for bit. You are simply taking a series of values like

100.24
120.56
099.77
000.33

(pretend that's the original 24 bit file)

and splitting them into two sets of numbers

100
120
099
000

(as in the 16 bit truncated file)

and

0.24
0.56
0.77
0.33

(as in the 24 bit difference file)

and then adding them back together again. Even I can get my head around that bit of maths!

sleeper1400 · 15th April 2009

Quote:

Originally Posted by Ozpeter

Unfortunately that's a very bad analogy. You are descending the mountain, not climbing it, for a start. The rest I'll address in the morning. It's very late here.

ummm. no.

his analogy was FLAWLESS. yours was a bunch of geek talk.

there is no need to even continue.

**Remoteness** · 15th April 2009

All due respect for everyone involved with this thread, but...

I find this thread fascinating and nauseating at the same time.

Is this even possible?

I want to stop reading it, but I seem to keep coming back to it every chance I get.

And, I'm getting dizzy each and every time I come back for more.
Man, I'm totally screwed with this.

We may need to shut this sucka down in a while; perhaps we should have a mandatory cut-off if the thread hits post number 437. Or should it be post 504?

Come on folks - let us get back to work or play or whatever you do when you're not on this thread.

Right or wrong?

Ozpeter · 15th April 2009

I really must do something else... but this is now how I see the whole thing in practical terms (and practical terms are what ultimately matters) -

When comparing a 16 bit recording vs a 24 bit recording, the level described in every sample in the 24 bit recording will be slightly more accurate than in the 16 bit recording (unless the sample happens to fall on a 16-bit-expressible value in the 24 bit recording).

The significance of the improved degree of accuracy can be considered as, or converted to, or heard as, audio or noise peaking to around -96dB below full scale. If the original audio is at a high level, then the significance (audibility) of something expressable as error converted to audio at that -96dB level may be felt to be in practice insignificant - that's a matter for individuals to decide on. As the original audio approaches -96dB, then the proportion of the error becomes more significant (audible), particularly when replayed at higher than normal levels. When the audio is entirely below -96dB then the 16 bit file is silent and therefore totally in error.

Using the truncation and inversion technique I described earlier, you can hear for yourself what the error actually sounds like for any given recording as if it had (by some ideal mechanism) been recorded at 16 bits instead of 24. The result is mostly quantisation noise but in a very good system there will be meaningful audio where passages in the original recording have levels below -96dB. However, in real world recording - particularly on location, getting back to our roots - such levels will rarely be encountered unless the recording level is set deliberately very low.

Ozpeter · 15th April 2009

Quote:

Come on folks - let us get back to work or play or whatever you do when you're not on this thread.

Right or wrong?

Well, it's been a valuable learning experience for me at least, right up till now. But I think I'm running out of steam...

Ozpeter · 15th April 2009

But we've not yet started on what the D to A converter actually does with these slightly incorrect samples and what happens if you try to scientifically analyse the actually reproduced sound of the 16 and 24 bit recordings... gulp...

**Remoteness** · 15th April 2009

Quote:

Originally Posted by Ozpeter

Well, it's been a valuable learning experience for me at least, right up till now. But I think I'm running out of steam...

I completely understand where you're coming from.

I guess we should keep this battle going until the "cops" show up.
Then we can scatter and re-group in another thread for one more blow-out-fest.

okydoky · 15th April 2009

Quote:

Originally Posted by Nishmaster

Thank you! It would appear that you are on the right page now. The increase in bit depth manifests itself solely as an increase in the available dynamic range, a decrease in noise. It is not more "accurate" in the sense of the word, which is the misconception that gets tossed around most often.

hi,

well, i have pretty much stayed on the right page. thank you very much for noticing!

the increase in bit depth does in fact result in greater accuracy at all levels. the 24 bit system is capable of registering and describing an amplitude value closer to the actual value presented to it than the 16 bit system is.

in that sense it is closer to being able to meet the requirements of the nyquist / shannon theorum. as we recall, one of the problems with the nyquist / shannon theorum is that it assumes an "infinite bit quantizer". as stated elsewhere,

"The assumptions necessary to prove the theorem form a mathematical model that is only an idealization of any real-world situation. The conclusion that perfect reconstruction is possible is mathematically correct for the model but only an approximation for actual signals and actual sampling techniques."

in any event, an increased ability to represent smaller quantization steps necessarily results in greater accuracy throughout the range with respect to amplitudes.

the increased accuracy does not manifest itself solely in the area below -96dBfs. this is well-established, and anyone trying [ad nauseum,, in this thread] to say that the increased accuracy in confined to levels below -96dBfs is misleading others, either deliberately or otherwise. there only seems to be one person trying to say that, unless you are also trying to say that.

what i am also saying is that this does not really have to be a "math problem".

and all the attempted analogies and so forth are confusing everyone even further.

and, respectfully, the way you write your posts is unduly difficult to decipher, because you assume that people are going to be able to follow your somewhat arbitrary, unclear manner of presentation.

i was unable to locate my secret decoder ring, so i did not actually even respond directly to your post.

but to the extent that you may be trying to argue that 24 bit audio does not capture amplitude more accurately than 16 bit audio, i disagree.

and i also think that some are kind of trying to turn this into a mathematics forum, rather than simply stating the obvious. i do not mean to complain, but its probably not very helpful to most of the readers to simply show off math skills over and over again, especially when you do not even seem to agree on what terms to use.

and bizarre experiments are not going to show anyone anything, particularly where they are undertaken in an attempt to prove someone's point.

i'm always interested, but my understanding has always been consistent with the pohlmann book, and this issue is long and very well established.

right.

okydoky · 15th April 2009

hi,

with regard to a couple of posts talking about "self-dither", i should mention that the prevailing thinking [for whatever that term may be worth to you] seems to be that relying on "self-dither" is a mistake.

circuit noise is not of the same nature as tpdf dither, or any other commonly used type of dither. circuit noise has a significant thermal noise component.

apparently for dither to really work well at all, it has to be a specific type of noise.

i am just reporting what i have heard from designers about this. i personally am not that crazy about the idea of adding a bunch of noise to signals unless it is really serving some purpose.

also, remember that you can generally perceive signal down into an analog noise floor [different than a digital noise floor].

right.

space2012 · 15th April 2009

http://en.wikipedia.org/wiki/Headroom
http://en.wikipedia.org/wiki/Dynamic_range
The dynamic range of human hearing is roughly 140 dB.
The dynamic range is defined as the ratio of the maximum to minimum amplitude a given device can record and is usually expressed in decibels.
The 16-bit Compact Disc has a theoretical dynamic range of 96 dB.
20-bit digital audio is theoretically capable of 120 dB dynamic range; similarly, 24-bit digital audio calculates to 144 dB dynamic range.
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.
Dynamic range in analog audio is the difference between low-level thermal noise in the electronic circuitry and high-level signal saturation resulting in increased distortion and, if pushed higher, clipping.
In 1981, researchers at Ampex determined that a dynamic range of 118 dB on a dithered digital audio stream was necessary for subjective noise-free playback of music in quiet listening environments.
"dBm" indicates that the reference quantity is one milliwatt, while "dBu" is referenced to 0.775 volts RMS.
http://en.wikipedia.org/wiki/Decibel
http://en.wikipedia.org/wiki/Signal-to-noise_ratio#Digital_signals
When using digital storage the number of bits of each value determines the maximum signal-to-noise ratio. In this case the noise is the error signal caused by the quantization of the signal, taking place in the analog-to-digital conversion.

http://en.wikipedia.org/wiki/Analog-to-digital_converter
ADC is an electronic device that converts an input analog voltage (or current) to a digital number.

The resolution of the converter indicates the number of discrete values it can produce over the range of analog values.

An ADC has several sources of errors. Quantization error and (assuming the ADC is intended to be linear) non-linearity is intrinsic to any analog-to-digital conversion. There is also a so-called aperture error which is due to a clock jitter and is revealed when digitizing a time-variant signal (not a constant value).
These errors are measured in a unit called the LSB, which is an abbreviation for least significant bit. In the above example of an eight-bit ADC, an error of one LSB is 1/256 of the full signal range, or about 0.4%.

ADC
resolution
in bitinput frequency1 Hz44.1 kHz192 kHz1 MHz10 MHz100 MHz1 GHz81243 µs28.2 ns6.48 ns1.24 ns124 ps12.4 ps1.24 ps10311 µs7.05 ns1.62 ns311 ps31.1 ps3.11 ps0.31 ps1277.7 µs1.76 ns405 ps77.7 ps7.77 ps0.78 ps0.08 ps1419.4 µs441 ps101 ps19.4 ps1.94 ps0.19 ps0.02 ps164.86 µs110 ps25.3 ps4.86 ps0.49 ps0.05 ps–181.21 µs27.5 ps6.32 ps1.21 ps0.12 ps––20304 ns6.88 ps1.58 ps0.16 ps–––2419.0 ns0.43 ps0.10 ps––––3274.1 ps––––––
This table shows, for example, that it is not worth using a precise 24-bit ADC for sound recording if we don't have an ultra low jitter clock. One should consider taking this phenomenon into account before choosing an ADC.

Since a practical ADC cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter performs a conversion (called the conversion time). An input circuit called a sample and hold performs this task—in most cases by using a capacitor to store the analog voltage at the input, and using an electronic switch or gate to disconnect the capacitor from the input. Many ADC integrated circuits include the sample and hold subsystem internally.

All ADCs work by sampling their input at discrete intervals of time. Their output is therefore an incomplete picture of the behaviour of the input.

If the input is known to be changing slowly compared to the sampling rate, then it can be assumed that the value of the signal between two sample instants was somewhere between the two sampled values. If, however, the input signal is changing fast compared to the sample rate, then this assumption is not valid.

If the input signal is changing much faster than the sample rate, then this will not be the case, and spurious signals called aliases will be produced at the output of the DAC. The frequency of the aliased signal is the difference between the signal frequency and the sampling rate. For example, a 2 kHz sinewave being sampled at 1.5 kHz would be reconstructed as a 500 Hz sinewave. This problem is called aliasing.

To avoid aliasing, the input to an ADC must be low-pass filtered to remove frequencies above half the sampling rate.

In A to D converters, performance can usually be improved using dither. This is a very small amount of random noise (white noise) which is added to the input before conversion. Its amplitude is set to be about half of the least significant bit. Its effect is to cause the state of the LSB to randomly oscillate between 0 and 1 in the presence of very low levels of input, rather than sticking at a fixed value. Rather than the signal simply getting cut off altogether at this low level (which is only being quantized to a resolution of 1 bit), it extends the effective range of signals that the A to D converter can convert, at the expense of a slight increase in noise

If a signal is sampled at a rate much higher than the Nyquist frequency and then digitally filtered to limit it to the signal bandwidth then there are 3 main advantages:

digital filters can have better properties (sharper rolloff, phase) than analogue filters, so a sharper anti-aliasing filter can be realised and then the signal can be downsampled giving a better result
a 20 bit ADC can be made to act as a 24 bit ADC with 256x oversampling
the signal-to-noise ratio due to quantization noise will be higher than if the whole available band had been used. With this technique, it is possible to obtain an effective resolution larger than that provided by the converter alone

. Thermal noise generated by passive components such as resistors masks the measurement when higher resolution is desired. For audio applications and in room temperatures, such noise is usually a little less than 1 μV (microvolt) of white noise. If the Most Significant Bit corresponds to a standard 2 volts of output signal, this translates to a noise-limited performance that is less than 20~21 bits, and obviates the need for any dithering.

The current crop of AD converters utilized in music can sample at rates up to 192 kilohertz. Many people[citation needed] in the business consider this an overkill and pure marketing hype, due to the Nyquist-Shannon sampling theorem.

high-profile recording studios record in 24-bit/192-176.4 kHz PCM or in DSD formats, and then downsample or decimate the signal for Red-Book CD production.

http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem
The theorem states:[1]

If a function x(t) contains no frequencies higher than B cps, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

The conclusion that perfect reconstruction is possible is mathematically correct for the model but only an approximation for actual signals and actual sampling techniques.
practice, neither of the two statements of the sampling theorem described above can be completely satisfied, and neither can the reconstruction formula be precisely implemented. The reconstruction process that involves scaled and delayed sinc functions can be described as ideal. It cannot be realized in practice since it implies that each sample contributes to the reconstructed signal at almost all time points, requiring summing an infinite number of terms. Instead, some type of approximation of the sinc functions, finite in length, has to be used. The error that corresponds to the sinc-function approximation is referred to as interpolation error. Practical digital-to-analog converters produce neither scaled and delayed sinc functions nor ideal impulses (that if ideally low-pass filtered would yield the original signal), but a sequence of scaled and delayed rectangular pulses. This practical piecewise-constant output can be modeled as a zero-order hold filter driven by the sequence of scaled and delayed dirac impulses referred to in the mathematical basis section below. A shaping filter is sometimes used after the DAC with zero-order hold to make a better overall approximation.

http://en.wikipedia.org/wiki/Sampling_frequency
sample rate, or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete signal.
The inverse of the sampling frequency is the sampling period or sampling interval, which is the time between samples.[1]
http://en.wikipedia.org/wiki/Clock_rate
http://en.wikipedia.org/wiki/Crystal_oscillator
12.288Digital audio systems - DAT, MiniDisc, sound cards; 256 × 48 kHz (28 × 48 kHz).
11.2896Used in compact disc digital audio systems and CDROM drives; allows binary division to 44.1 kHz (256 × 44.1 kHz), 22.05 kHz, and 11.025 kHz

http://en.wikipedia.org/wiki/Bit_rate
http://en.wikipedia.org/wiki/PCM
http://en.wikipedia.org/wiki/Audio_bit_depth
For a recording with a 44.1 kHz sampling rate, 2 channels (stereo) and a 16 bit depth:
44100 x 2 x 16 = 1411200 bits per second, or, 1411.2 kbit/s
dynamic range in dB is equal to bits * 6.02 + 1.76.
'bit' is the abbreviation for a single 'binary digit', represented by a 0 or a 1. Since a digital 'word' is simply a binary number, the number of bits per word is simply the number of digits that make up the corresponding number.
Binary numerics are base-2; thus, each digit can only be a '0' or a '1'. In comparison, traditional decimal numerics are base-10, having digits that can only be 0 through 9. For example, the 16-bit binary number '1001011011001010' is equivalent to the 5-digit decimal number 38602.
http://en.wikipedia.org/wiki/Digital_audio
In an analogue audio system, sounds begin as physical waveforms in the air, are transformed into an electrical representation of the waveform, via a transducer (for example, a microphone), and are stored or transmitted. To be re-created into sound, the process is reversed
its fundamental wave-like characteristics remain unchanged
All analogue audio signals are susceptible to noise and distortion, due to the inherent noise present in electronic circuits.
All analogue audio signals are susceptible to noise and distortion, due to the inherent noise present in electronic circuits.
http://en.wikipedia.org/wiki/Digital-to-analog_converter

Maximum sampling frequency: This is a measurement of the maximum speed at which the DACs circuitry can operate and still produce the correct output.
it is necessary to use DACs that operate at over 40 kHz. The CD standard samples audio at 44.1 kHz,
http://en.wikipedia.org/wiki/Sample_rate_conversion
http://en.wikipedia.org/wiki/Oversampling

http://www.mother-of-tone.com/creation.htm
Altmann Creation ADC is the world's first zero-oversampling high sample-rate audio AD converter.
No analog or digital filters. -90 dB background hiss
Altmann Creation ADC uses a true 16-bit sampling topology without any filtering and without any digital processing. todays analog to digital converters employ 1-bit or low bit sampling. Todays other AD converters with their low-bit topology perform a time-averaging AD conversion which is subject to mathematical interpretation.
A REAL AD conversion, as performed by the Altmann Creation ADC is not subject to interpretation, but it is a real precision measurement of the analog input signal.

space2012 · 15th April 2009

download this 96kHz test-signal, however it will look distorted when played back on your oversampling DAC.

to record with 44.1kHz sample-rate.
The Altmann Creation ADC will record this step-function as it occurs, although it contains higher than Nyquist frequencies.
When this recording is played back on a non-overampling DA-Converter, like the Altmann Attraction DAC, it looks like this:

This looks pretty much like the input signal, just a little bit more course, because of the slower 44.1 kHz sample rate (remember, the analog input signal was generated with 96kHz).
Now, what happens, if we do the same recording and playback, but use any of today's common ADC and DAC topologies with low-bit resolution and oversampling,as they are employed in every recording studio on this planet ? Well, it then looks like this:

The difference you see, is in the ripple that occurs before and after every step-event. This ripple-distortion is caused by the internal digital filtering
Whenever a musical transient is recorded, it will be distorted just like shown in the above measurement.
Your ears hear this added 'ripple' and it causes the music to sound unnatural or artificial.
the following scopeshot. This was recorded with the Altmann Creation ADC, and played back through a common oversampling DA-Converter:

As you see, the Altmann Creation ADC reduced the ripple-distortion significantly, although the playback is performed by a conventional oversampling DAC.

But thers no other A/B audio files to hear/download, same source signal vs. other ADC.
strange.
The Altmann Attraction DAC
Digital to analog conversion is performed by a R2R converter operating on true sample-rate (no oversampling) and true sample-values. This means, that the data on the disc (input data) is converted sample-by-sample with high precision and without altering any data.
http://en.wikipedia.org/wiki/Oversampling
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.
By increasing the bandwidth of the sampled signal, the anti-aliasing filter has less complexity and can be made less expensively by relaxing the requirements of the filter at the cost of a faster sampler.
, oversampling is implemented in order to achieve cheaper higher-resolution A/D and D/A conversion. For instance, to implement a 24-bit converter, it is sufficient to use a 20-bit converter that can run at 256 times the target sampling rate. Averaging a group of 256 consecutive 20-bit samples adds 4 bits to the resolution of the average, producing a single sample with 24-bit resolution.
averaging is possible only if the signal contains perfect equally distributed noise (i.e. if the A/D is perfect and the signal's deviation from an A/D result step lies below the threshold, the conversion result will be as inaccurate as if it had been measured by the low-resolution core A/D and the oversampling benefits will not take effect)..
a signal with a bandwidth or highest frequency of B = 100 Hz. The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at 200 Hz would result in β = 1. Sampling at four times that rate (β = 4) would result in a sampling rate of 800 Hz. This gives the anti-aliasing filter a transition band of 600 Hz ( (fs-B) - B
(800Hz-100Hz) - 100Hz
600 Hz) instead of 0 Hz if the sampling frequency was virtually 200 Hz.
An anti-aliasing filter with a transition band of 600 Hz is much more realizable than that of 0 Hz (which would require a perfect filter). If the sampler went to eight times over then the transition band would increase to 1400 Hz, which means the anti-aliasing filter could be less expensive due to relaxation of the transition band requirements.
After being sampled at 800 Hz, the signal (ostensibly with a bandwidth of 400 Hz) could be digitally filtered to have a bandwidth of 100 Hz and then further downsampled to closer to 200 Hz.

d_fu · 15th April 2009

Sorry Steve, one last try...

Quote:

Originally Posted by Ozpeter

When comparing a 16 bit recording vs a 24 bit recording, the level described in every sample in the 24 bit recording will be slightly more accurate than in the 16 bit recording (unless the sample happens to fall on a 16-bit-expressible value in the 24 bit recording).

Incorrect...

Please forget about dBs. Think voltages. Look at David's math and also forget about noise floors for now:

A standard audio ADC requires 2V peak to peak to light up all the bits.
16 bits = .0305 mV = -96 dBFS = lowest resolvable signal component
24 bits = .00012 mV = -144 dBFS = lowest resolvable signal component

A 16 bit converter will divide the range from 0 to 2 V into 65536 steps, i.e. equal steps of 0.000030517578125 V or 0.0305 mV. Any level and any amplitude variation below that (e.g. 0.01 mV) will not be "seen", regardless of the absolute amlitude at any given time.

A 24 bit converter divides the same range (0 - 2 V) into 16 million "steps", of 0,00000011920928955078125 V or 0.00012 mV. Any amplitude variation at any absolute position can be increased or decreased by a value as small as 0.00012 mV, e.g. from 2 V to 1,99999988079071044921875 V. This is not limited to the range below -96 dBFS.

Quote:

The significance of the improved degree of accuracy can be considered as, or converted to, or heard as, audio or noise peaking to around -96dB below full scale.

In a way, yes. But it is not limited to that range.

Quote:

Using the truncation and inversion technique I described earlier,

I would consider this test to be quite unscientific and thus meaningless, as it involves the use of plugins (the behaviour of which at low levels you know nothing about). You could have a software generate a sine wave with a fade in 16 and 24 bit instead

Quote:

The result is mostly quantisation noise but in a very good system there will be meaningful audio where passages in the original recording have levels below -96dB. However, in real world recording - particularly on location, getting back to our roots - such levels will rarely be encountered unless the recording level is set deliberately very low.

In real world recording, there is no such thing as audio with a dynamic range of 96 dB. The advantage you get out 24 bit is indeed that lower level settings will be sufficiently far from the converter's noise level...

Quote:

Originally Posted by oky****

with regard to a couple of posts talking about "self-dither", i should mention that the prevailing thinking [for whatever that term may be worth to you] seems to be that relying on "self-dither" is a mistake.

Maybe, but my point was that in a normal live recording, you're not likely to ever encounter quantization noise (unless you set max. levels at -70 dBFS), even with a 16 bit recording. Ambient noise takes care of that, levels won't likely fall anywhere near even -90...

Audiop · 15th April 2009

Quote:

Originally Posted by oky****

hi,
initially, we are not talking about "narrower" impulse responses, we are talking about "taller" ones [amplitude]. the greater amplitude is what alleviates the problem with pre and post ringing. the issue of narrower impulse responses giving an advantage in localization of sounds is separate, and has been debated and contested.

Hi oky****!

I think the way you put it is confusing and it would be more correct to talk about faster sampling having higher bandwith which means it has better slewrate. It can track the fast signals better. It does not truly alleviate the ringing (for an identical filter with higher samplerate) but put the ringing higher in frequency.

What is your source for improved impulse response (as long as the system has the full audio bandwith) giving an advantage of localization?

I think it can be worthwhile to point out that transients (pulsive sounds) end up with right timing even with 44.1kS/s.. in other words the peak of the transient does not have to end up at a point of sampling but it can end up between as well. One needs to understand "the sinc" and the nature of lowpass filters for that.

Quote:

its generally agreed that ringing is bad, and pre-ringing is troublesome in particular, because it is not something that is found in nature, and analog audio has not historically suffered to any extent from pre-ringing, or anything like it. but all filters ring.

Some filters are free from ringing I reckon.. such as first order butterworth filters and some Bessel functions. Non resonant/ringing filters are called aperiodic if memory serves me.

Quote:

the "argument" being made is that you are basically getting more back from the system at 192kHz than you are at 44.1, or 96, at least in terms of impulse response.

Yes, a higher sample rate will always result in higher bandwith which means improved timedomain performance as well as frequency response. These are two sides of the same coin and they follow.

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there is a better impulse response with faster sampling. this is true in the typical band of interest as well as in "supersonic" frequencies. so you do not have to record square waves yielding harmonics above 20kHz to realize the improved impulse response.

Strictly speaking, I think not. If you feed a bandwith limited signal (one that has no information at the nyquist frequency or above) there will be no ringing. Ringing is appearant with material that has significant energy in the upper range around the filter cut of.

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i am not sure if you are saying that subsequent sample rate conversion from e.g. 192kHz to 44.1kHz "destroys" the improved impulse response, or not [or to what extent].

Don't know if this was sorted out but yes it does. There's no improvements in impulse response when going down to 44.1kS/s from 192kS/s.

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i'm sure you have considered that most anyone doing recordings at 192kHz would be keeping tracks and mixes archived at that bit depth.

Guess it was a typo but since this can be confusing enough as it is I'd like to point out that "192kHz" is not about bit depth but sample rate.

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i agree that, to my knowledge, bit depth does not appear to impact impulse response. at least i have never heard anyone say that it did.

Correct, it doesn't!

/Peter

space2012 · 15th April 2009

Anti-aliasing - Wikipedia, the free encyclopedia
anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution signal at a lower resolution.
Anti-aliasing means removing signal components that have a higher frequency than is able to be properly resolved by the recording (or sampling) device. This removal is done before (re)sampling at a lower resolution. When sampling is performed without removing this part of the signal, it causes undesirable artifacts such as the black-and-white noise near the top of figure 1-a below.
anti-aliasing is often done using an analog anti-aliasing filter to remove the out-of-band component of the input signal prior to sampling with an analog-to-digital converter.
Figure 1-a illustrates the visual distortion that occurs when anti-aliasing is not used. Notice that near the top of the image, where the checkerboard is very distant, the image is impossible to recognize, and is not aesthetically appealing. By contrast, figure 1-b is anti-aliased. The checkerboard near the top blends into gray, which is usually the desired effect when the resolution is insufficient to show the detail. Even near the bottom of the image, the edges appear much smoother in the anti-aliased image. Figure 1-c shows another anti-aliasing algorithm, based on the sinc filter, which is considered better than the algorithm used in 1-b. Figure 2 shows magnified portions of Figure 1 for comparison. The left half of the image is taken from Figure 1-a, and the right half of the image is taken from Figure 1-c. Observe that the gray pixels help make 1-c much smoother than 1-a, though they are not very attractive at the scale used in Figure 2.

Compare the diamond on the left with the anti-aliased one on the right

Enlarged view

Figure 3

Fig 3 shows how anti-aliasing smooths the outline. Text is affected in just the same way.

(a)

(b)

(c)Figure 1

Figure 2

. Reconstruction filter - Wikipedia, the free encyclopedia
a reconstruction filter (or anti-imaging filter) is used to construct a smooth analogue signal from the output of a digital to analogue converter (DAC) or other sampled data output device.
The sampling theorem describes why the input of an ADC requires a low-pass analog electronic filter, called the anti-aliasing filter. For the same reason, the output of a DAC requires a low-pass analog filter, called a reconstruction filter. Ideally, both filters should be brickwall filters, constant phase delay in the pass-band with constant flat frequency response, and zero response from the Nyquist frequency.
Practical filters have non-flat frequency or phase response in the pass band and incomplete suppression of the signal elsewhere
in theory a DAC gives a series of impulses, in practice, the output of a DAC is more typically a series of stair-steps. The low pass reconstruction filter smooths the stair step (removes the harmonics above the Nyquist limit) to (re)construct the analogue signal corresponding to the digital time sequence.
Nyquistâ€“Shannon sampling theorem - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Samplin...nal_processing)
Digitizing - Wikipedia, the free encyclopedia
Anti-aliasing filter - Wikipedia, the free encyclopedia

Metric system - Wikipedia, the free encyclopedia
1microvolt is 1⁄1,000,000 of a of a Volt.
0 dBu = 0.775v
thermal noise is less than 1microvolt.
16-bits is 65.536
20-Bits is 1.048.576
24-Bits is 16.777.216

audio bit-depth is limited by thermal noise. but...
Sampling Rate is not limited by thermal noise.
but by wordclock jiter.
192khz at 24-Bits, needs 0.10ps of maxium jitter.

Second - Wikipedia, the free encyclopedia
1 picosecond is 10–12 seconds. = 0,00000000001
converter needs to do oversampling.

jitter is limited by crystal quality, accuracy, temperature, and electric ripple & noise...
also if its an external clock, also limited by cable quality, purity of the materials, size, shield, etc...

why record at 24-Bits if thermal noise limits to 20-Bits?
easy... becouse at 24-Bits, still theres more resolution even if thermal noise only allows to see 20-Bits, theres less steps in those same "20-Bits of dynamic range & noise floor" at 24-Bits, theres no need for dither, becouse the LSB is not truncated, etc..

sampling rate is two things at same time, limits the maxium frequency range. "vertical", and horizontal, the maxium of splits/steps/sampling points 1 second of audio can have.
if you split 1 second in 1trillion, you get verry accurate picture, but assuming theres no jitter, becouse that is limited by clock jitter.

44.100 is needed for 22050hz audio bandwith,
44.100x16x2 = 1.411.200 data rate,
88.200x16x2 = 2.822.400 data rate,
192.000x24x2 = 9.216.000 data rate.

transfer rate is more than double, becouse the Biphase Mark Code.
Biphase mark code - Wikipedia, the free encyclopedia

Acoustics - Wikipedia, the free encyclopedia

Ozpeter · 15th April 2009

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I would consider this test to be quite unscientific and thus meaningless, as it involves the use of plugins (the behaviour of which at low levels you know nothing about). You could have a software generate a sine wave with a fade in 16 and 24 bit instead

The generation of the audio file to be tested comes before the test, so cannot invalidate its results. You suggest using a software tone generator to create a fading sine wave. I used a software tone generator (a VSTi) to create a fading music note - quite deliberately, because I suspected that if I had used a sine wave, then someone would have said 'ah, but sine waves do not have the harmonic content of musical instruments' - hey ho, I can't win.

Let me repeat - you can take any 24 bit file, however it was created, truncate it to 16 bits, invert that against the original, and you will have the difference between the two, which will consist of the content of the least significant 8 bits of the 24 bit file. Where the stripped-off most significant 16 bits were greater than zero, the remaining 8 bits will sound as noise - not surprisingly as they are not meaningful without the original data contained in the original most significant 16 bits. Where the original most significant 16 bits were zero, then the whole of the original signal is preserved in the remaining 8 bits, and whatever audio is present in those samples can be heard because no change was made by the inversion. When the sub-96dB difference file is mixed with the 16 bit file, you get the original 24 bit file back, bit for bit. If you think this is wrong, don't say so till you've tried it yourself, I would respectfully request. So far the test has been attacked on the basis that there's something wrong with the DAW(s) used, and now that there's something wrong with the file used. There is nothing wrong with the DAW or the file, nor the test.

I have not the slightest doubt that the use of 24 bits provides a lower noise floor throughout a recording. What I still doubt is whether the benefit of the added resolution at all levels translates to anything other than that lower noise floor, as some appear to imply (and some assert it directly). If terms such as 'more air' or 'less compressed' or 'wider stereo image' (quoting David from memory, and picking on him because he has made the most specific claims, as I recall it!), or 'greater resolution', are synonyms for 'lower noise floor', then I think it's important to just use that description, otherwise there's a danger that some may think there's some other quality which can be heard and described - or even analysed.

chris319 · 15th April 2009

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What I still doubt is whether the benefit of the added resolution at all levels translates to anything other than that lower noise floor, as some appear to imply

The benefit is when you normalize/maximize/apply digital gain, whatever you want to call it, i.e. boosting levels in the digital domain by multiplying all samples by a given factor.

If you record 24-bit audio with peaks at -48 dBFS and then boost the levels digitally by 48 dB, you essentially have the equivalent of a 16-bit recording made with peaks at 0 dBFS. The benefit of recording at 24 bits and peaks at -48 is that you have 48 dB of headroom as a safeguard against clipping.

okydoky · 15th April 2009

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Originally Posted by Audiop

Hi oky****!

I think the way you put it is confusing and it would be more correct to talk about faster sampling having higher bandwith which means it has better slewrate. It can track the fast signals better. It does not truly alleviate the ringing (for an identical filter with higher samplerate) but put the ringing higher in frequency.

hi,

i don't think that we are talking about only slew rate here.

and i actually think you may be talking about something quite different than i am, or at least a different aspect. see below.

faster sampling involves greater bandwidth, which yields better amplitude impulse response. this is separate than time / frequency domain stuff, although they are also improved.

you appear to be referring exclusively to time / frequency domain response, and that is not what i was talking about, nor is it what the graph that was posted is intended to convey.

there are many kinds of impulse responses that can be tested for a given system, and i believe that they do not all interrelate the way that time / frequency domain does.

you are talking about fourier, maybe?

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