# What sampling rate and bit depth would be necessary to make a digital recording indistinguishable from the original?

I'm assuming this is a solved question (please cite sources).

It seems like a 96kHz sampling rate with 24-bit samples is standard for high-resolution audio, but is this considered to be indistinguishable from natural audio?

• possible duplicate of Max audio sample rates? though we may want to actually flip it around since this question is more detailed. Either way, a merge is probably in order. Commented Apr 23, 2014 at 15:32

## 5 Answers

The sample rate of audio and video are two different things.

# Video's Frames Per Second (fps)

In video, a frame (sample) rate of 24fps is required to prevent flickering. The common frame rates (25 and 30) has to do with the fact that early televisions used the mains frequency for the purpose of syncing (50Hz in the UK, 60HZ in the States). The primary reason for higher frame rates is the reduction of motion blur. To my knowledge, latest research suggests that somewhere between 90Hz-112Hz the effect is no longer recognisable.

# Audio's Sample Rate

The sample rate of digital audio relates to the highest frequency captured/reproduced. As the Nyquist Theory states:

A signal can be perfectly captured and reconstructed, so long the signal is band limited and sampled at equal intervals at a frequency at least twice the highest frequency present.

Thus, a 44,100Hz sample rate can accommodate a signal with frequencies up to 22,050Hz. A 40000Hz sample rate can accommodate a signal with frequencies up to 20,000Hz

Following a debate, the 44,100 Hz figure was chosen as the best compromise between various requirements, including those of the various television standards at the time. This sample rate was subsequently used with audio CDs.

However, analogue-to-digital conversion (ADC) technology in the 1980s still exhibited distortion at levels that could be reduced using higher sample rates. Thus, when the DVD standard was established, the sample rate of 48,000 was chosen; representing a higher-fidelity audio.

The limitations in technology at the time are no longer part of modern ADC, where nearly all converters use 1-bit oversampling.

# Human Hearing Range

The audible human hearing range is quoted as 20Hz - 20,000Hz (20kHz). Not a single empirical experiment in history has shown that any human being is capable of hearing frequencies above 20kHz. This is attributed to the density of the high-frequency 'hair' cells in our ears and the maximum rate at which they fire.

It is also worth noting that about more than half the population above the age of 45 is incapable of hearing frequencies above 16kHz.

# Inaudible Frequencies can Yield Audible Ones

However, any signal being converted from digital to analogue must pass through a non-linear system before it reaches our ears. The obvious example of such system is the speaker cone. When audio passes through a non-linear system, distortion is created in the form of additional frequencies. Under such conditions, frequencies above 20kHz can actually result in distortion below 20kHz. However, unless the non-linear system is fundamentally faulty, for programme material (normal typical everyday sounds - not a loud sin wave of 30kHz) the distortion created is inaudible.

The same principle applies when digital audio is processed in a non-linear fashion within a digital system. Distortion content above 20kHz will be generated, and depending on the sample rate, it may alias back to the audible range.

The last two paragraphs explain why it is sometimes justified to use sample rates higher than 44,100.

# ADC Frequency Headroom

To answer your question directly, the required limit of sampling rate (while only accounting for human hearing) is 40,000Hz.

However, before sampling, convertors need to filter audio content above 20,000Hz. Since the effect of all filters is gradual (they cannot simply remove everything above a particular frequency, they only attenuate it gradually), convertors need some headroom to sufficiently remove content above 20,000Hz. Thus, a sample rate higher than 40,000Hz is always required.

# Conclusion

While 40,000Hz represents the theoretical max sample rate required with humans, ADC technology still requires some headroom above this figure.

With modern ADC technology, 44100Hz is perfectly capable of capturing material up to 20,000 Hz.

From a game development point of view, you should not worry about this aspect.

• For final delivery, some have argued that going much over 44,100 is actually bad ( evolver.fm/2012/10/04/…) However this excellent answer is correct to point out that higher sample rates can be justified durring production.
– Bjorn Roche
Commented Sep 19, 2013 at 17:54
• Adding a lot of ultrasonic frequencies, like using higher than 96 kHz sample rates, is detrimental because those frequencies are basically just a crapstorm of noise that increases file size. Ok, If the crapstorm just would stay confined to the high frequencies it wouldn't matter because we wouldn't hear it. But real world imperfections, such as nonlinearities in the audio path, and the mother of all evil: resampling without proper low pass filters, can translate it to tones that are in our hearing range. That makes some of the noise and crap audible to us. Some say that it enriches the sound.
– PkP
Commented Aug 12, 2016 at 17:59

With 96kHz sampling, the acoustic spectrum that can be "recorded" without error (nyquist criteria etc..) is from 0Hz to about 44kHz. The spectral range that a human can hear is the text-book "20Hz to 20kHz" so, one should be able to say that scientifically 96kHz is pretty good. In fact 44kHz (CDs etc.) should be able to cope with 20kHz as well so no problem there on the face of it....

24bits means the signal is quantized to "2 raised to the power of 24" different numerical digital values. I'll do the math - If full scale were 2 volts peak to peak then a digital resolution of 0.12 micro volts results - that's a lot less than a good signal received on an FM antenna from your local radio station 10 miles away. 24 bits is a really good resolution and the electronic guys have worked out that the slight "error" you might get gives you a signal to noise ratio of 144 dB. The error I refer to is the "approximation" (or quantization) error when digitizing an analogue signal into a digital number. 144 dB signal to noise is pretty much like hearing an ant walk across a piece of paper while watching the TV. OK I'm using potentially provocative metaphors here but look at the range of hearing a human can hear...

0dB SPL is the threshold of hearing and 144dB SPL is beyond pain.

So, 96kHz sampling and 24 dB sample resolution should be OK. Is it OK? It's fine for me but I still read articles that: -

• Talk about the ultrasonic artefacts getting lost when sampling at too low a frequency i.e. 44kHz
• Say aliasing of ultrasonic artefacts cause problems at mid range audio
• Tell of people using really, really expensive speaker cables (to ostensibly counter skin effect) so that they can "appreciate" the spectrum way above the recognized audio limits of humans.
• There appear to be audiophiles who compare pretty decent op-amps from the usual vendors and summising all sorts of nonsense between supplier A and supplier B - ya know, stuff that if you read the data sheet would/should not affect things one little bit.
• People want amplifiers with remarkably low distortions like 0.0001% (about 74 dB Sig/Noise) when they don't seem to bother much about the doppler shift of frequencies in their speakers giving about 1% aural distortion.
• The list goes on so to prevent this being a tirade against the audiophile population I'll shut up.

You decide.

The range of human hearing is typically 20-20K Hz if I remember correctly, and this is why CD audio was set at 44100. To properly reconstruct a signal, you need to have approximately 2x the sample rate of the maximum frequency (see: Nyquist-Shannon sampling theorem). 44100 was picked as a value that gave acceptable quality reconstruction within the file storage budget they had at the time (~750MB for an album)

Frequencies outside the human-hearing range can still interfere constructively and destructively to color the audible frequencies, so people (at least informally) suggest using equipment which can handle such frequencies. This would be the reason why 48K and 96K are used: they can capture a wider range of frequencies.

side note: the CMYK print standard for images is usually quoted as 300dpi and this is because it is 2x the 150-line screens used for plate making in high-quality print publications. Again, sampling rate twice the frequency to avoid artifacts and moire.

• +1 great description of the correlation between human hearing and sampling rates.
– Byte56
Commented Sep 19, 2013 at 15:54

16bit 44,1KHz is alaready supposed to be like natural audio.

My thought are that the resolution isn't so important compared to the choice of microphone, microphone placement, preamplifier, way of working and mixing your record and speakers in which you are listening.

Working in 96kHz 24 bits surely allows to have more headroom and to process sound easily but it doesn't garrantee to have à record which sound natural.

Have a nice day :)

Clem

Good question, Zach. No sample rate nor any bit depth can make any recording indistinguishable from natural sound. This is due to both the simple fact that you will loose some vital information in any recording, and also due to imperfections in any replay system. Did you ever do a stereo mic recording in a room where you where present yourself, and after you wondered why the recording has a lot more acoustics/reverb on it than you can remember? When we are present in a room our selective hearing is working and we "select" what to focus our hearing on. Hence we "deselect" unwanted sounds, like room acoustics. As soon as we do a recording to two tracks this selectivity disappears. This has to do with a number of parameters, and many attempts have been made to recreate the exact impressions from the live situation. The closest to date may be the binaural recording technique - https://en.wikipedia.org/wiki/Binaural_recording - But the best listening experience for these recordings imply that you use headphones(!) So, what I'm trying to say is that one should do recordings as good as one can, and with a quality that is reasonable for the purpose of the recording. Maybe someone else can give you an answer as to what sample rate or bit depth that will recreate sound waves so that our ears theoretically can not distinguish them from natural sound, but your recordings will never be fully natural.