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Correlation between sample rate and audible frequency?

milezone

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#1
I often read, in widely published and observed articles, and 'reputable sources' etc. e.g. this one: https://www.sweetwater.com/insync/7-things-about-sample-rate/. claiming that sample rate is somehow correlated to the audio frequency spectrum and that since humans don't hear above 20khz there's no reason to strive for high sample rates in music recording.

As I understand it, a sample rate is the speed at which an ADC or DAC pulls or renders packets of audio information as defined by bit size from or into an audio signal. In the case of DSD the packet size is one bit hence the high sample rate.

A sample rate of 1hz at 1bit in my understanding would only be able to pull one (or two?) bit of information every second. Therefore a faster sample rate with a higher bit depth is always more desirable -- in the case of a discrete function pulling from a continuous source of information -- the higher the sample rate and bit depth, the more information get's pulled or rendered. That said there is a threshold in my experience where the benefits of higher sample rates are imperceptible, although that's to be determined by the listener. And furthermore as far as I understand, I'm unaware of any correlation between this perception of quality and the fact that the upper human hearing threshold is ~20khz.

A 44.1khz 24bit recording should roughly equal the resolution 1.056mhz 1bit DSD recording right?

This article touches on some of the points which I may be confused about:

https://homerecording.com/bbs/equip...ons/dsd-vs-pcm-head-engineer-phillips-179930/

In any case I'm hoping to better understand the relationship between perceived audible frequency and sample rate if there is one.
 
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ahofer

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#2
I thought @March Audio posted a good video on this over at the Harbeth User Group. I can’t seem to find it right now.

[email protected] posted it below.
 
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PaulD

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Milezone, there are a number of points to your post. First I'd suggest spending the 20 mins watching Monty's Digital Audio Show & Tell here
I have watched it many times and there is usually something new to find in it!

There might be reasons to use higher sample rates than 44.1KHz or 48KHz, as the phase response drifts from flat much earlier than the frequency magnitude response. This was more more true in the early days of analogue filters than it is today. Note that there is very limited evidence that phase anomalies are audible.

Also, for the production of a recording (the actual recording and editing of it), then working at a higher sample rate and bit-depth makes certain sense as it allows for margins of error that are not needed for final distribution. So it is common these days to record at 96KHz and 24-bit, even if final distribution is in 16/44.1.

You are right, there is a threshold above which higher sample rates are imperceptible. Even experienced mastering engineers (I'm quoting Bob Katz here) say they cannot reliably tell the difference between a 96KHz recording and a properly downsampled 44.1KHz version. Note that Bob claims with some credibility that he can usually tell the difference between 16-bit and 24-bit final masters, particularly if the dithering has not been properly done, and the program material lends itself to that.

DSD is 1-bit recording at a higher sample rate. 1-bit recording has a dynamic range of 6dB (suboptimal). 24-bit PCM has a dynamic range of 144dB, greater than we need. DSD achieves acceptable noise performance by aggressively "noise shaping" the noise to the ultrasonic region above the audio band. DSD was developed long before 24/96 PCM became easily achievable...

There are a lot of claims made for DSD that are not supported. I did try the early Korg DSD recorder in a studio and it sounded no better than the standard (Digidesign) PCM version of the signal (no conversion done between the digital streams, level-matched and single-blind).

For me (opinion here), I cannot see the point of DSD except as a marketing ploy and for copy protection. DSD digital streams cannot be edited at all, they must be converted to PCM and then back to DSD, which the purists point out defeats the purpose...

To your final point, there is very little to no evidence that a frequency response above 20KHz is useful (certainly not for consumer quality audio), and, so a sample rate of 44.1KHz is fine for distribution.
 
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amirm

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#4
High sample rate allows higher bandwidth but one is not forced to use it. So yes, if all you want to capture is 1 Hz bandwidth, you can run any sample rate you like and results will be the same. It is just that up to a point, by convention as sample rates are doubled, so is the bandwidth that is allowed. A 96 kHz sampling allows 48 kHz of bandwidth. A 44.1 kHz sampling allows 22.05 kHz and so on.

At a sample rate of 192 kHz though, some DACs may roll off some of that extra bandwidth and not give you 96 kHz for example which is fine since we can't hear that high anyway.
 

KozmoNaut

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#5
Also, for the production of a recording (the actual recording and editing of it), then working at a higher sample rate and bit-depth makes certain sense as it allows for margins of error that are not needed for final distribution. So it is common these days to record at 96KHz and 24-bit
.
Specifically, a higher sample rate allows for lower latency, which is usually measured as X number of samples. This can be important for lining up everything or if you're monitoring directly while recording. It also allows super high frequency results from effects to land naturally, and be dealt with later.

The bit depth is generally more important. Every step of the way, every effect and EQ cut/boost, every ADC/DAC in the chain adds a little bit of cumulative noise. You obviously want to keep that noise as low as possible, for a better final result.
 

PaulD

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Latency can be important for overdubs, but one usually just reduces the IO buffer size, the SR is not so important, or rather it's fixed... For live digital systems the SR is more important than mixing, as there's no way to change the buffer to minimise the latency. Yes, it's usual to align all of the drum mics with the overheads and so on.

ProTools these days is 64-bit floats internally which is practically impossible to underflow or overflow, so the internal digital effects (EQ etc) are without losses. ADC/DAC pairs (eg for going to external effects) are practically transparent now, unless misused or faulty.
 
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#8
So does the steep low pass @20khz (reconstruction filter?) affect the audible range or not. That Montgomery fella limits the discussion by just saying digital filters are better than analog ones (duh!).

"Because digital filters have few of the practical limitations of an analog filter, we can complete the anti-aliasing process with greater efficiency and precision digitally. The very high rate raw digital signal passes through a digital anti-aliasing filter, which has no trouble fitting a transition band into a tight space. "
 

Blumlein 88

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#9
Try downsampling everything to 44.1kHz and to check if you can hear a difference. I highly doubt it.
See attached PDF in zip form. Amandine Pras at McGill University.

Very well done blind test with excellent gear. Minimalist recordings. People didn't hear a difference in 88.2 and 44.1. They did hear a difference in 88.2 downsampled to 44.1 it seems. I've in the past done positive ABX identification of some downsampling. It is an analog-esque way of thinking, but listening to the exact format the recording was done has its pluses.

Oddly many at hydrogen audio thought the proper way was to record everything at 192 and down/upsample. In this test they ran parallel processors at the two rates. I think hydrogen audio whiffed on this one.
 

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Blumlein 88

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So does the steep low pass @20khz (reconstruction filter?) affect the audible range or not. That Montgomery fella limits the discussion by just saying digital filters are better than analog ones (duh!).

"Because digital filters have few of the practical limitations of an analog filter, we can complete the anti-aliasing process with greater efficiency and precision digitally. The very high rate raw digital signal passes through a digital anti-aliasing filter, which has no trouble fitting a transition band into a tight space. "
Depends upon the digital filter. Some of the popular audiophile filters with slow rolloffs let too much imaging and aliasing occur. Plus if you are young enough to have good high frequency hearing they droop the upper octave enough to be audible. Good steep filters won't be a problem. Flat enough response to 20 khz and steep filtering to keep the audible band clean of artifacts.
 

PaulD

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I'd forgotten about that paper. Sample rate converters can vary with quality, although I would have through that most of the major ones these days we're transparent. Here's a comparison of many http://src.infinitewave.ca
 

Blumlein 88

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I'd forgotten about that paper. Sample rate converters can vary with quality, although I would have through that most of the major ones these days we're transparent. Here's a comparison of many http://src.infinitewave.ca
Me too, but you never know. Especially quite a few DAW's have built in resamplers that aren't too great even now. If you can find any of the jangling keys recordings done by the late Arny, I could ABX his files. When I took his high sample rate file and resampled to 44.1 khz with Sox, I could no longer ABX it. Don't know what he used, but it was sub-standard. Oh, and I could only do that with good headphones. Couldn't do it with speakers.
 

amirm

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#13
If you can find any of the jangling keys recordings done by the late Arny, I could ABX his files.
I could too: :)

foo_abx 1.3.4 report
foobar2000 v1.3.2
2014/07/09 06:32:02

File A: C:\Users\Amir\Music\Arnys Filter Test\keys jangling band resolution limited 4416 2496.wav
File B: C:\Users\Amir\Music\Arnys Filter Test\keys jangling full band 2496.wav

06:32:02 : Test started.
06:33:07 : 01/01 50.0%
06:33:17 : 02/02 25.0%
06:33:24 : 03/03 12.5%
06:33:36 : 04/04 6.3%
06:33:47 : 05/05 3.1%
06:33:58 : 06/06 1.6%
06:34:12 : 07/07 0.8%
06:34:15 : Test finished.

----------
Total: 7/7 (0.8%)

-----
 

BDWoody

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#14
A sample rate of 1hz at 1bit in my understanding would only be able to pull one (or two?) bit of information every second. Therefore a faster sample rate with a higher bit depth is always more desirable -- in the case of a discrete function pulling from a continuous source of information -- the higher the sample rate and bit depth, the more information get's pulled or rendered.
What helped me was a better understanding of Nyquist-Shannon...

More samples don't necessarily give you a more accurate reconstruction. Common sense says more dots let's you connect the dots more smoothly, but sampling and reconstruction doesn't work that way.
 

daftcombo

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Me too, but you never know. Especially quite a few DAW's have built in resamplers that aren't too great even now. If you can find any of the jangling keys recordings done by the late Arny, I could ABX his files. When I took his high sample rate file and resampled to 44.1 khz with Sox, I could no longer ABX it. Don't know what he used, but it was sub-standard. Oh, and I could only do that with good headphones. Couldn't do it with speakers.
Can we conclude that it is a matter of bad resampling, not a matter of sample rate?
 

Pluto

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#16
I often read, in widely published and observed articles, and 'reputable sources' etc. claiming that sample rate is somehow correlated to the audio frequency spectrum and that since humans don't hear above 20khz there's no reason to strive for high sample rates in music recording
There is a factor often avoided in this discussion. Superficially, higher sampling rates lead to larger bandwidth and a consequent need for less intrusive filters so that approach must be good, regardless of the limitations of the human ear. Right?

Not necessarily. The higher the sampling rate, the greater the necessary precision in nearly every subsystem within the converters and the harder it becomes to make measurements of sufficient accuracy. The Uncertainty Principle tells us this. At a lower clock rate, and A to D converter has more time available to obtain a stable (and therefore reliable) measurement. If I give you a multimeter and ask you for an average measurement of the mains voltage over a one minute period, the task is straightforward. If I want to know that voltage over a particular millisecond, it's a far harder task. It is generally easier to measure something when you have more time in which to do it.

Simplistic thinking suggests that the higher the clock frequency, the more accurate the ultimate waveform recovery (owing to a higher number of data points) and this is true, up to a point. But there will certainly come a frequency where the INaccuracy of measurement inherent in ever-increasing clock rates becomes counter-productive and the ultimate result, less good.

The big question is, at what clock rate does the reduced quality of measurement outweigh the provision of more data points?
 

Zog

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#17
I have a question that might be related. When one generates a square wave is that not done with a formula that can include frequencies well above 20 Khz? I have seen a demonstration that shows the 'top' of the square wave to actually be a fine sine wave. So my question is this: If these square waves could be played and listened to then are we in effect listening to sound above 20 Khz? Also my understanding is that the overtones of many instruments go beyond 20Khz - maybe 30Khz or so. Their amplitude would be surely small but, like the 'square' wave they would have an impact on the lower frequencies.
 

KozmoNaut

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#18
Try it! If you have a system with 192KHz (or higher) sample rate support, try generating some square waves in a program like Audacity, and see what happens as you increase the base frequency.

(If you can't hear the overtones, because they're ultrasonic, it just sounds like a sine wave)
 

Zog

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#19
(If you can't hear the overtones, because they're ultrasonic, it just sounds like a sine wave)
My thinking is that the ultrasonic sounds are not separate. What comes out of the speaker is a single sound (let's assume a single speaker cone). It may be made from multiple frequencies - all music is - but the higher and lower frequencies combine. In the audible spectrum you could produce a sinewave at 440hz. Call that exhibit A. Then simultaneously play 440 hz and 700 hz - exhibit B. You hear something different. The waveform if you were to convert that to a drawing would no longer be a sine wave - it would be different. Now extrapolate that so that so that exhibit A is made from a note just within hearing - say 18Khz and a combination of 18Khz and 24Khz would be exhibit B. Now will they sound the same?
 

milezone

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I appreciate the straightforward explanations.

As I understand, audio signal from source to speaker is a single waveform comprised of infinite overtones in an analog state. Because sampling occurs in the time domain, the greater the frequency of sampling = greater resolution. So a byproduct of higher sample rates is the capacity to reconstruct higher audible frequencies? Is this of secondary importance to data resolution achieved through higher sample rates? If not, would 20khz 1bit recording be a sufficient standard?

An analogy is a video camera which records a more accurate picture/captures more information when shooting at higher frames per second. In this analogy color bit depth is similar to higher bit depth per sample in an audio example = greater resolution of the reconstructed waveform.

For all intents and purposes 48khz 24bit conversion may be a suitable for audio applications though I'm not certain the 20khz human hearing limit is relevant to why.

The first half of this video is informative, the second half theoretical but interesting:

 
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