Back to basics. Definition: Analogue audio

[Fleuch]

For N bits the number of values is 2^N, so for 8 bits you actually have 256 values. The number of steps is one less, e.g. 255 for 8 bits, since you do not include the "ground floor" (the range of values for an unsigned 8-bit converter is 0 to 255).

The definitions that I and others have used for decades:

• Analog = continuous in time and amplitude
• Sampled-analog = discrete time or amplitude, other parameter continuous
• Digital = discrete in time and amplitude

Loosely, analog is a continuously-varying signal without discrete time or amplitude (voltage, current, power, displacement, whatever) values. Digital is numerical with values quantized in amplitude and time (thus chosen from a fixed, discrete set of values). Sampled-analog applies to things like a sample-and-hold (or track-and-hold) that quantizes in time but not in amplitude. Bucket-brigade delay lines and CCD imagers are sampled in time but not in amplitude. The delay line's output is usually applied to an analog amplifier, essentially staying sampled-analog in nature, whilst an imager's cells usually feed an ADC and so are quantized (digital) after conversion. A basic comparator without a latch (i.e. no clock) will quantize in amplitude but not in time -- it flips whenever the signal crosses a threshold.

These are pretty fundamental definitions used by standards bodies like the IEEE, at least when I was involved with such things.

FWIWFM - Don

This is the clearest definition of the difference between analog and digital signals. With these definitions it is perfectly logical to describe DC as an analog signal, even if it is at a predefined zero. it simply means that the amplitude of a DC signal does not vary with time.

A sampled analog signal is distinct from a quantised signal. When the sampled analog signal is quantised it is assigned a specific value using an appropriate modulo counting system, where binary, octodecimal, decimal, and hexadecimal are commonly used examples. This leads to considering a digital binary signal as having only two quantisation levels. Where the sampled analog signal exceeds the amplitude assigned to the two quantisation levels, further digital binary signals are required to represent the this amplitude. For example an 8-bit Analog to Digital Converter has 256 possible output combinations using 8 separate digital binary output lines, where the signal on each of those lines is confined to one of two amplitudes. The output of the the ADC is a quantised signal representing the sampled analog signal at the input, it is not a digital binary signal but a combintion of 8 separate digital binary signals.

The distinction between the three distinct categories listed in the original post needs to be clearly understood as there seems to be a degree of misapprehension around quantisation and digital binary signals.

Note that there is no mention in the definitions of confining the analog, sampled analog or digital binary signal within any given parameter. The definition of the digital signal states clearly that it is discrete in time and amplitude. An octodecimal representation of a signal, for example, requires eight discrete levels in the discrete time period, whereas the implication in the original definition is that it is a digital binary signal being described. In the context of current usage, "digital" is automatically equated with "binary".

For what it is worth, the guiding principal of ASR is to assess the accuracy of a "black box" to reproduce a signal (in whatever medium) at the output, where the format of the input and output signals may be different.

 

[Ken Tajalli]

This is the clearest definition of the difference between analog and digital signals. With these definitions it is perfectly logical to describe DC as an analog signal, even if it is at a predefined zero. it simply means that the amplitude of a DC signal does not vary with time.

A sampled analog signal is distinct from a quantised signal. When the sampled analog signal is quantised it is assigned a specific value using an appropriate modulo counting system, where binary, octodecimal, decimal, and hexadecimal are commonly used examples. This leads to considering a digital binary signal as having only two quantisation levels. Where the sampled analog signal exceeds the amplitude assigned to the two quantisation levels, further digital binary signals are required to represent the this amplitude. For example an 8-bit Analog to Digital Converter has 256 possible output combinations using 8 separate digital binary output lines, where the signal on each of those lines is confined to one of two amplitudes. The output of the the ADC is a quantised signal representing the sampled analog signal at the input, it is not a digital binary signal but a combintion of 8 separate digital binary signals.

The distinction between the three distinct categories listed in the original post needs to be clearly understood as there seems to be a degree of misapprehension around quantisation and digital binary signals.

Note that there is no mention in the definitions of confining the analog, sampled analog or digital binary signal within any given parameter. The definition of the digital signal states clearly that it is discrete in time and amplitude. An octodecimal representation of a signal, for example, requires eight discrete levels in the discrete time period, whereas the implication in the original definition is that it is a digital binary signal being described. In the context of current usage, "digital" is automatiaclly equated with "binary".

For what it is worth, the guiding principal of ASR is to assess the accuracy of a "black box" to reproduce a signal (in whatever medium) at the output, where the format of the input and output signals may be different.

Just a quick observation:
- this argument is limited to Audio.
- Signal by definition and assumption must carry information. if it doesn't , then it is either noise, distortion or some other unwanted artifacts.
-by the above, steady DC maybe analogue or not, since it does not carry audio information, it is not of importance.
- Analogue is a relative phrase, the signal needs to be analogous relative to another signal.
By those points, a continuously changing signal analogous to another, is classed as analogue audio.
If it is not analogous to another signal, then it is not.
Sampled data, measured against a numerical table, is digital.
My 2 pence.

 

[Fleuch]

Just a quick observation:
- this argument is limited to Audio.
- Signal by definition and assumption must carry information. if it doesn't , then it is either noise, distortion or some other unwanted artifacts.
-by the above, steady DC maybe analogue or not, since it does not carry audio information, it is not of importance.
- Analogue is a relative phrase, the signal needs to be analogous relative to another signal.
By those points, a continuously changing signal analogous to another, is classed as analogue audio.
If it is not analogous to another signal, then it is not.
Sampled data, measured against a numerical table, is digital.
My 2 pence.

Perhaps it is wise to further define what a signal actually is.

Unwanted signals, such as electromagnetic interference / pickup or ground "noise", are interpreted by a "black box" as a valid input and processed in the same way as a "wanted" signal. In the digital domain timing errors and other related discrepancies also lead to "unwanted" deviations from the original pulse train.

Quite simply, whether a signal carries information or not is of no consequence to the "black box", only to the designer / manufacturer / operator of the equipment. A "black box" is unable to discriminate between "wanted" and "unwanted" information. Noise, distortion, timing errors and other unwanted artifacts are processed by the "black box" in the same way as the "wanted" audio information. In other words, whether or not a signal carries "information", this leads to a definition that is far too narrow. The definition of a signal must surely be expanded to include "unwanted" signals in whatever format that will be processed together with the "meaningful" audio information.

When defining "sampled data, measured against a numerical table" as "digital" means that some form of conversion on the sampled signal has already taken place to convert it from the analogue domain to the digital domain. The output of a sample and hold circuit is analogous relative to the amplitude of another signal (the input) at a specific instant of time; it is a "snapshot" of a signal amplitude at that specific instant of time. A sampled signal is therefore analog until converted to multi-bit digital format. It seems that using the definition "Sampled-analog = discrete time or amplitude, other parameter continuous" identifies the function of a sample and hold circuit but does not apply to sampled data after conversion to the digital domain.

A digital pulse train has a finite amplitude for a finite time period, although that time period is determined by another signal, where the shape of the pulse is important. It is not an analogue of another signal but does it meet the definition "Analog = continuous in time and amplitude" as strictly it is continuous in time and varies continuously in amplitude between one of two values, where information is conveyed both by amplitude and time. Is pulse width modulation digital, as information is again conveyed by both amplitude and time?

In serial transmission of digital "information" the definition "Digital = discrete in time and amplitude" again has problems. An oscilloscope trace of a pulse train shows it as a continuous waveform continuous in both amplitude (although ideally only at two pre-determined levels) and time. This applies when using voltage levels to represent the pulse train, but does it apply where a carrier waveform is required as in optoelectronics, or Bluetooth and WiFi? Does it apply in parallel transmission where the signal consists of multi-bit binary digital signals that have to be interpreted as a group?

The transmission of a pulse train is subject to the same physical contraints as a continuous analog signal, but the difference lies in how any signal is interpreted, or how information is conveyed by each signal. On a purely physical level where, for example, the attenuation and propagation delay of either a "digital" or "analog" signal is considered in the same transmission medium, there is no difference. An analog signal can take an ifinite number of values between two limits whereas a binary digital signal can only take one of two discrete values at instances of time defined by some form of clock signal. Regarding signal propagation there is absolutely no difference; the difference lies in the interpretion of the information conveyed in the format of each signal.

If this seems pedantic, it only illustrates the problem and difficulty of deriving fundamental definitions for different formats of signals used in the reproduction of audio information.

 

[radix]

Digital audio is sampled and quantized data. It's a data format. It is independent of how one transfers it.

Most modern communication systems are not square wave or simple 1 pulse per bit. They convert the data (e.g. the digital audio, likely in something like PCIe or Ethernet encapsulation) into data symbols that are transferred as complex (in the I-Q sense) digital signals that really look more like analog than old school digital.

 

[tomtoo]

Its just a question of interpretation of the data. If you say a 1khz sin is a one and 5khz is a 0. The signal is analog but your interpretation is digital. Every good old 300baud modem could show you this.
All this is done, we send terra bits/s without failure. We can interprete digital data very good, far above what we need for hearing, And i have no need for discussion only couse some people have no plan what they talk about.

 

[rgpit]

Specifically for the recording, storage, and playback of audio, take an audio signal, apply a binary number to represent the signal's amplitude with regard to time and store it. To reconstruct the original signal, read back the binary numbers with respect to time and write the signal that is represented. Everything else is analog.

 

[Ken Tajalli]

Perhaps it is wise to further define what a signal actually is.

Good idea.

Unwanted signals, such as electromagnetic interference / pickup or ground "noise", are interpreted by a "black box" as a valid input and processed in the same way as a "wanted" signal. In the digital domain timing errors and other related discrepancies also lead to "unwanted" deviations from the original pulse train.

Although technically correct, but what does it matter? Digital sampling was designed to separate wanted data from unwanted signals! am I right?
For as long as these unwanted signals do not interfere with data retrieval, they may as well not exist!
If timing errors occur because of unwanted noise or bad impedances, then we need to make sure they don't.
Noise is an Analogue signal, because it is directly related to other signals, and freely changing.

Quite simply, whether a signal carries information or not is of no consequence to the "black box", only to the designer / manufacturer / operator of the equipment. A "black box" is unable to discriminate between "wanted" and "unwanted" information. Noise, distortion, timing errors and other unwanted artifacts are processed by the "black box" in the same way as the "wanted" audio information. In other words, whether or not a signal carries "information", this leads to a definition that is far too narrow. The definition of a signal must surely be expanded to include "unwanted" signals in whatever format that will be processed together with the "meaningful" audio information.

Depends on your definition of black box. A digital receiver successfully segregates data signal from unwanted signals, because data is coded, noise is not.
The Voyager spacecraft's digital signal, still reaches earth, from beyond the solar system, riddled with noise, yet the earth stations successfully decipher the data, in this case, the black box being the receiver array together with all the receiving computers.

When defining "sampled data, measured against a numerical table" as "digital" means that some form of conversion on the sampled signal has already taken place to convert it from the analogue domain to the digital domain. The output of a sample and hold circuit is analogous relative to the amplitude of another signal (the input) at a specific instant of time; it is a "snapshot" of a signal amplitude at that specific instant of time. A sampled signal is therefore analog until converted to multi-bit digital format. It seems that using the definition "Sampled-analog = discrete time or amplitude, other parameter continuous" identifies the function of a sample and hold circuit but does not apply to sampled data after conversion to the digital domain.

You lost me there, all I am saying is that the codes generated as digital audio, only have discrete levels against , not undefined values with time, which copies another signal.

A digital pulse train has a finite amplitude for a finite time period, although that time period is determined by another signal, where the shape of the pulse is important. It is not an analogue of another signal but does it meet the definition "Analog = continuous in time and amplitude" as strictly it is continuous in time and varies continuously in amplitude between one of two values, where information is conveyed both by amplitude and time. Is pulse width modulation digital, as information is again conveyed by both amplitude and time?

An analogue audio signal, by your explanation, is indistinguishable from induced noise, the black box can not tell them apart.
A digital audio signal, in be it PCM or PWM, is indeed distinguishable from induced noise, and that is the beauty of it.

I have run out of steam!

 

[xaviescacs]

Somehow this hasn't been brought up either here or in the other thread, but it's analog which just the approximation.

The universe is quantized all the way down - matter, energy, time, and space.

It's just that usually the individual quanta are so small compared to the scale one is working at that it's easier to treat values as continuous.

I would like to address some quick words (from memory) to this important subject. xD

Some things are quantized, others are not, or not as one can imagine reading such statements. To begin with, space and time to the present day haven't been proved to be quantized. There are models and conjectures, but I've heard of no experiment to refute that space or time are continuous. There are examples of space or angular momentum quantization, but that's not the same as saying that space in the universe is intrinsically quantized, it means that in some situations the measure of a spatial quantity gives only certain values (Stern–Gerlach experiment).

One example is an electron in an hydrogen atom. It can only have certain levels of energy which depend on the potential created by the proton (and other details, depending on how rigorous one wants to be), so we say the energy is quantized, because it can only have certain levels, namely, when we measure it we always get one of those values (this is ideally, there are corrections due to spin-orbit interaction and other things I don't remember xD, reality is always more complicated). When one solves the equation, the energy of the electron can have only certain values, but for each of those energy levels, the state of the electron that describes its position is a continuous function. There are "soft" restrictions to its position, there are points more likely than others, but no point is prohibited. Moreover, if we measure the position of such electron, it can have any value, so it's not quantized.

Another interesting case is the spin of an electron that serves as quantum bit. The spin of the electron, when we measure it, it can have two values, up and down (or whatever two names), but the qbit does its job because if we don't measure it, and if the state of the electron is a superposition of both pure spin states, then the quantum state of the electron has 2 degrees of freedom (Bloch sphere) , and that allows for quantum computing etc. So the values it can take when we measure it are a closed set, in this case two, but the state that describes it is continuous due to the superposition of pure states.

So everything is quantized? Well, is not that simple.

 

[maverickronin]

I would like to address some quick words (from memory) to this important subject. xD

Interpretations of QM are essentially modern metaphysics and I don't even play a physicist on TV, but right now I'm basically going with the option that space and time are quantized at the level of of the Planck length/time which when combined with individual particles of quantized mass/charge/etc would
quantize all interactions.

 

[radix]

Interpretations of QM are essentially modern metaphysics and I don't even play a physicist on TV, but right now I'm basically going with the option that space and time are quantized at the level of of the Planck length/time which when combined with individual particles of quantized mass/charge/etc would
quantize all interactions.

Hawking's calculation was 1/4 nat of information per plank area. At least for the information density of a black hole.

 

[Fleuch]

A voltage or current waveform propagated in any transmission medium is subject to the same laws of physics. In this respect alone there is no difference between a voltage (or current) waveform that represents a varying amplitude or a varying frequency or a varying pulse train. This is fundamental.

In a similar way light and sound will also be subject to the laws of physics when propagated in any transmission medium.

The difference is in the way the waveforms are interpreted by an observer, whether it is information, as interpreted by the observer, or unwanted interference or noise.

The title of the thread is "Back to basics. Definition: Analogue audio". From the physical structure of the human auditory system all perceived audio signals must be analogue as a pulse train carrying information will not be interpreted as a meaningful input to that system.

It is in the way audio information is recorded, interpreted and reproduced that differences exist, where the input to this process, is analogue audio and the output from this process is analogue audio, with respect to the human auditory system. No doubt the time will come when some form of artificial intelligence will be able to directly interpret a received pulse train.

 

[Fleuch]

Digital audio is sampled and quantized data. It's a data format. It is independent of how one transfers it.

Most modern communication systems are not square wave or simple 1 pulse per bit. They convert the data (e.g. the digital audio, likely in something like PCIe or Ethernet encapsulation) into data symbols that are transferred as complex (in the I-Q sense) digital signals that really look more like analog than old school digital.

Agreed there are various forms of modulation which are not simple 1 pulse per bit ( https://www.rohm.com/electronics-basics/wireless/modulation-methods, or https://en.wikipedia.org/wiki/Modulation for example) but it is difficult to understand how data as symbols is transmitted.

 

[tomtoo]

Agreed there are various forms of modulation which are not simple 1 pulse per bit ( https://www.rohm.com/electronics-basics/wireless/modulation-methods, or https://en.wikipedia.org/wiki/Modulation for example) but it is difficult to understand how data as symbols is transmitted.

Its just importend that you can differ, under given cirumstanses, good between a 0 and a 1.

 

[radix]

Its just importend that you can differ, under given cirumstanses, good between a 0 and a 1.

Agreed there are various forms of modulation which are not simple 1 pulse per bit ( https://www.rohm.com/electronics-basics/wireless/modulation-methods, or https://en.wikipedia.org/wiki/Modulation for example) but it is difficult to understand how data as symbols is transmitted.

The main idea of digital communications is that one uses quantized values. One can use various decoding techniques to decide which quantized value was intended with channel noise and distortion and attenuation. Simple encoding schemes, like NRZ, Manchester, biphase mark (used in AES/SPIDF), 8b/10b, are square wave-ish encodings at 2x the clock rate [EDIT: 8b/10b is not 2x clock rate] so the receiver can recover the clock from the data. Some minimize DC offset by having equal numbers of high and low voltages or using positive and negative voltages. High-speed digital communications use more efficient clock recovery or use multiple bits per clock. Most (all?) high-speed systems use symbols, not data bits. Symbols could be, for example, 8b/10b encoding or could be more complex symbol sets (e.g. 16 QAM, 64 PAM). But in all these cases, one is able to remove most all digital signal noise because the decoder can find the closest quantized value. When using multiple bits per clock (symbols), one can decode to the closest symbol.

The important thing is even if the digital signal is highly distorted, so long as one can decide on the right symbol the underling digital audio data (and thus its analog representation) remains as good as it can be.

 

[j_j]

While I understand what people are trying to convey, what one usually calls "digital" audio is a quantized, sampled ANALOG of the original pressure wave or intended pressure wave.
Likewise, what we call 'analog" is a continuous-time, continuous-level ANALOG of the original pressure wave or intended pressure wave.

Sampling can be done without quantization and used to be exceptionally common in telephony systems, wherein "TDM" (time domain multiplexing) was used to put many calls over one wider-band circuit.

Sampling requires limiting the signal bandwidth to under 1/2 of the sampling rate, for conventional sampling methods. When some one samples a signal, and knows the sampling rate, then one knows exactly when to "reconstruct" a sample. In a normal "analog" system (using the term as usually used in an audio system) the "time" is not precise, and subject to both noise and quantum effects, and therefore can never EVER be known exactly. This means if you resample, reconstruct again, and repeat a few more times, system noise will grow due to the error in sampling and reconstruction.

Quantization, which CAN be done without sampling, but which usually isn't (see "flash converters" for more on that), quantizes the LEVEL of the signal, meaning that it reduces the necessarily noisy signal amplitude (noise enforced by thermal noise, shot noise, current noise, charge on the electron, ALL OF WHICH ARE SIGNIFICANT AT NORMAL AUDIO LEVELS!!!!) to a set of levels. This means that you know, given the level of a sample, exactly what you need to reproduce that sample with.

So, a "digital" stream, meaning quantized and sampled, then can be reproduced exactly to the level of accuracy it was recorded at, given proper reproduction equipment. The sequence of levels can be copied to another file, another disc, what-have-you WITH NO FURTHER LOSS. In a system with continuous levels (i.e. analog) you will get a different measurement every sample, thanks to the fundamental nature of the universe, yes, really. So this is a second reason that "analog" can not be losslessly reproduced. Every generation must be worse. There is no other outcome. Copying the OUTPUT of the proper reproduction equipment does not, however, result in lossless reproduction, as there will be (physics always wins) error in the continuous-time, continuous-level domain. Always.

How the sequence of levels are encoded is not an issue. Yes, twos-compliment binary is useful, and 6db/bit for a uniform quantizer (meaning each step is the same height) is a useful tool for what the resulting SNR will be in a system. (barring oversampling and noise shaping, see 'advanced topics' when somebody gets around to bugging me to give that talk again and have it recorded this time)

The fact you have precisely KNOWN levels and precisely KNOWN times is why digital can be copied accurately.


What's most common for delivery is 16 bit uniform quantization at one of 44.1, 48, 88.2 or 96 kHz. 16/44 is redbook CD.

Any properly operating 16 bit system exceeds the best accuracy in any standard tape recorder or LP by a substantial amount. As digital copying is in fact lossless (unless you process the samples somehow, which can happen) it is also frequency flat to the extent of the filters that properly limit its bandwidth. This is a very simple, testable assertion.

Now, in the modern day, people are arguing for more than 48kHz sampling rate, which may or may not (evidence is lacking but not entirely rejectable out of hand given a good understanding of the hearing apparatus and its nonlinear behavior) be necessary, but which should not do harm as long as it's done properly. Do remember that doubling the sampling rate more than doubles the signal path complexity, though. I can not imagine a sampling rate higher than 64kHz should matter in any case, at least for human beings. Cats,dogs, and bats are another story.

Now, about bit depth. Having a wider bit depth can be argued to be necessary, and when done properly, can not hurt in acquisition of a recording under any circumstances, as long as it's done properly.

There are some "gotchas" there, of course. The noise level due to the air molecules striking your ear drum is 6dB SPL to 8.5 dB SPL, white noise, 20-20k. The hearing apparatus can ad about another 15 dB or so due to filtering, and another 5.5 due to detection abilities, so that drops that level to about 6-20, or -14dB SPL. Interestingly that level is ***JUST*** below the threshold of hearing at any frequency. I do not personally find this surprising. So calling that -15dB SPL, and bearing in mind most systems can't reach more than maybe 110dB SPL, even under the absolute best of all worlds, 120dB (yes, I'm rounding) would be more than sufficient. That's 20 bits. For most systems, something like 18.5 bits is more than enough, even assuming your listening room is perfectly isolated. In most listening situations, you aren't even close to 16 bits (seriously!).

So generally, 16 bits, properly produced, should suffice for most people in their homes. For cars and portable, even 16 bits is a massive overkill.

But there's more. Thanks to the charge on the electron, if you want a signal to noise ratio of 'n' (in linear scale, not log scale) you need n^2 electrons to go through your circuit per second.

I will leave it to you to consider the current output necessary from a microphone to reach 16, 20, 24, and 32 bits. I don't mean the current after a pre-amp,but the actual change in current from the capsule itself (or for an RF condenser, or such, the detector circuit).

For video, the differences in eye sensitivity create a very different set of requirements, complicated by viewing distance rather than sound intensity.

 

[j_j]

On the issue of how to REPRESENT the sequence of levels, that is, assuming it's not foolishly done, is not an issue that matters. PCM is usually represented by twos-compliment binary, but that's not a requirement, nor is it necessary to represent those levels with a fixed bit length. (Hence lossless encoders/decoders that take advantage of various redundancies.) All that's required is the knowledge of what level to output at the next sample instant.

 

[antcollinet]

(barring oversampling and noise shaping, see 'advanced topics' when somebody gets around to bugging me to give that talk again and have it recorded this time)

Thanks for that description - very helpful.

Is there an accessible archive anywhere of your talks that have been recorded

 

[j_j]

Thanks for that description - very helpful.

Is there an accessible archive anywhere of your talks that have been recorded

www.aes.org/sections/pnw

Look at the 'meeting recaps'. There are also ppt decks (or pptx depending on when) for those that have not been recorded.

 

[antcollinet]

www.aes.org/sections/pnw

Look at the 'meeting recaps'. There are also ppt decks (or pptx depending on when) for those that have not been recorded.

Excellent - thanks. Going away for the w/e, will have a look when I get back.

 

[Fleuch]

While I understand what people are trying to convey, what one usually calls "digital" audio is a quantized, sampled ANALOG of the original pressure wave or intended pressure wave.

The sound pressure wave is first detected and then converted to another physical quantity in an "analogue" format which is a representation of the original prior to recording. The recording process may be "analogue" or "quantised digital" where the quantised value may be pure binary or in one of many codes, such as that used over a USB connection.

Whether the signal representing the original sound pressure wave is "analogue" or "digital", the interpretation depends on the source and the receiver. A pulse in a "digital" system is essentially an analogue signal with only two recognised values. It is the interpretation of the information encoded in the signal that differentiates "analogue" and "digital" systems.

Between the source and the receiver the information conveyed by the signal, whether analog or digital, is subject to the same laws of transmission derived from the laws of physics. Quoting from a previous post "A voltage or current waveform propagated in any transmission medium is subject to the same laws of physics. In this respect alone there is no difference between a voltage (or current) waveform that represents a varying amplitude or a varying frequency or a varying pulse train. This is fundamental."