What Sample Rate Do We Really Need?

compact disc, dacs, mp3 players and streaming audio
NOYB
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What Sample Rate Do We Really Need?

Post by NOYB » 24 Oct 2019 06:09

Lets say a 11025 Hz sine wave is sampled at 44.1 KHz (4 times the sine wave frequency). Lets also say that the samples are at the mid point of each rise and fall (above and below 0) of the sine wave (~50% of the sine wave peaks). So 4 samples per cycle are captured with values that are half that of the signal level.

When played back the DAC can reproduce that frequency (11025 Hz). As it is only 1/4 the sample rate. But how does the DAC reproduce the original sine wave from those 4 samples?

joedisco
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Re: What Sample Rate Do We Really Need?

Post by joedisco » 24 Oct 2019 07:27

Hi, well, Im perhaps the last person prepared to answer such a question but I remember my old elementary classes in mathematical modeling... Remember the Fourier transform... It has been a long, long, long time since I ever applied any knowledge related to it

But perhaps you have heard about the Nyquist Shannon Theorem which is based on Fourier Analysis and Fourier Synthesis... Superposition principle and all that... I vaguely remember!

Well, in fact I don't pretend to have the knowledge to answer your question but I just hope to point in the right direction and other people far smarter than me will come to clarify...

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Re: What Sample Rate Do We Really Need?

Post by aardvarkash10 » 24 Oct 2019 08:26

vinyl aficionados will say digital is of the devil and they can hear the slicing sounds made by the sampler as it cuts and dices the waveform into artificial disjointed segments of demonic pulses.

Me - I figure that the Philips book got it pretty right. I suspect very few people, if any, could reliably pick the standard rate from an alternative, higher rate. You can try yourself on down sampling and work out where it is that you start noticing degraded sound quality in that direction.

NOYB
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Re: What Sample Rate Do We Really Need?

Post by NOYB » 24 Oct 2019 10:14

aardvarkash10 wrote:
24 Oct 2019 08:26
vinyl aficionados will say digital is of the devil and they can hear the slicing sounds made by the sampler as it cuts and dices the waveform into artificial disjointed segments of demonic pulses.

Me - I figure that the Philips book got it pretty right. I suspect very few people, if any, could reliably pick the standard rate from an alternative, higher rate. You can try yourself on down sampling and work out where it is that you start noticing degraded sound quality in that direction.
The question is intended to be more about the objective technical aspects than subjective philosophical, hearing, perception, etc.

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Re: What Sample Rate Do We Really Need?

Post by Erin1 » 25 Oct 2019 12:24

Simple answer:

The low pass filter in the output stage of the DAC will filter out the sharp edges of the stair steps resulting in a smooth analogue sine wave.

Note: only R2R DACs have "stair step" outputs. Newer Delta Sigma DACs don't have stair steps.

Further note: all DACs designed for audio including the R2R variety have an output filter, so the analogue output will never have steps or pulses. It will just be a sine wave (or analogue audio signal)

The filter smooths the samples.

There is a mathematical answer to your question. But I'm not great at calculus.
If you read up on the Nyquist Shannon theorem you will get a better idea.
You only need 2 samples to reconstruct the signal.

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Re: What Sample Rate Do We Really Need?

Post by Erin1 » 25 Oct 2019 12:40

NOYB wrote:
24 Oct 2019 10:14
The question is intended to be more about the objective technical aspects than subjective philosophical, hearing, perception, etc.
Please see my response above. But also don't forget that empirical observation has revealed the Nyquist Shannon sampling theory to work in practice as well as in theory.

To elaborate a little more.. if the output of an R2R (resistor ladder) DAC is not filtered you still get audio, but you also get the 44100khz pulses coming out of the analogue outputs (RCA sockets). This causes aliasing (read up on aliasing too)


So very steep analogue filters were used in early CD players to filter the 44100khz frequency, bit there is a frequency drop at 20khz. Caused by the mathematical equation sinc(x)

So to avoid aliasing, oversampling was invented and the filters could be at a higher frequency and less steep but achieve the same result and a flat frequency response and less no phase change in the audio spectrum.

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Re: What Sample Rate Do We Really Need?

Post by Erin1 » 25 Oct 2019 13:06

NOYB wrote:
24 Oct 2019 06:09
. Lets also say that the samples are at the mid point of each rise and fall (above and below 0) of the sine wave (~50% of the sine wave peaks). So 4 samples per cycle are captured with values that are half that of the signal level.
In this unlucky example you've given the sampled waveform wouldn't precisely resemble the input waveform... but you're only talking about 4 samples. You can't even hear 4 samples if they were played back. You wouldn't even hear a blip, or pop. 😉 4 samples would be like a mosquito flapping one wing once.
In time 4 samples is 1(second) / 44100 x 4 = 907 micro seconds. (Is that correct??)

The likelihood that an audio waveform over a period of one second would all be falling at the mid point of the samples is so unlikely to be not worth being concerned about.

Don't forget for CD, the sampling is done at forty four thousand, one hundred times per second!
Can you count to 44,100 in one second? No, of course not. It's really, really fast!

But in the real world fortunately we have a tendency to be more lucky than unlucky and music audio waveforms are not actually sine waves, they are highly complex and unpredictable wiggles. So the ADC has a really good chance of capturing an accurate (enough) representation of what went into it.

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Re: What Sample Rate Do We Really Need?

Post by Shadowman82 » 29 Oct 2019 00:58

Strictly digitally speaking the article I posted in the "why can't digital sound as warm as analog" thread does suggest that some people can tell the difference between CD quality and digital of a higher resolution than CD . I would say 24-bit/96khz is sufficient . I'd also argue that DSD at the standard SA-CD resolution is sufficient as well even though it works a bit different from say PCM or FLAAC .

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Re: What Sample Rate Do We Really Need?

Post by Hanuman » 29 Oct 2019 13:54

NOYB wrote:
24 Oct 2019 06:09
Lets say a 11025 Hz sine wave is sampled at 44.1 KHz (4 times the sine wave frequency). Lets also say that the samples are at the mid point of each rise and fall (above and below 0) of the sine wave (~50% of the sine wave peaks). So 4 samples per cycle are captured with values that are half that of the signal level.

When played back the DAC can reproduce that frequency (11025 Hz). As it is only 1/4 the sample rate. But how does the DAC reproduce the original sine wave from those 4 samples?
Is easier (and more accurate) to imagine the samples as points the sine wave must pass through. When you’ve got that concept then it’s easily to see that the peak-to-peak swing of the samples is not necessarily the same as the peak-to-peak swing of the sine wave.
Last edited by Hanuman on 29 Oct 2019 14:37, edited 2 times in total.

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Re: What Sample Rate Do We Really Need?

Post by Hanuman » 29 Oct 2019 14:23

Erin1 wrote:
25 Oct 2019 12:40
But also don't forget that empirical observation has revealed the Nyquist Shannon sampling theory to work in practice as well as in theory.
It's a theorem, not a theory. That makes it a provable rule.

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Re: What Sample Rate Do We Really Need?

Post by Hanuman » 29 Oct 2019 14:34

Erin1 wrote:
25 Oct 2019 13:06
In this unlucky example you've given the sampled waveform wouldn't precisely resemble the input waveform... but you're only talking about 4 samples.
It wouldn't matter where, relative to the waveform, the samples are taken. The samples are not the waveform. They are code given to the DAC to enable it to reconstruct the waveform.

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Re: What Sample Rate Do We Really Need?

Post by TubularBell » 29 Oct 2019 15:16


NOYB
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Re: What Sample Rate Do We Really Need?

Post by NOYB » 30 Oct 2019 07:16

MQA part 1; Why 24 bit 192 kHz audio?
https://www.youtube.com/watch?v=r_wxRGiBoJg

MQA part 2: how does MQA work
https://www.youtube.com/watch?v=T5o6XHVK2HA

The truth about Nyquist and why 192 kHz does make sense
https://www.youtube.com/watch?v=geaoEt-9V-w

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Re: What Sample Rate Do We Really Need?

Post by Hanuman » 30 Oct 2019 13:16

NOYB wrote:
24 Oct 2019 06:09
Lets say a 11025 Hz sine wave is sampled at 44.1 KHz (4 times the sine wave frequency). Lets also say that the samples are at the mid point of each rise and fall (above and below 0) of the sine wave (~50% of the sine wave peaks). So 4 samples per cycle are captured with values that are half that of the signal level.
This premise is wrong. Those conditions can't be met for a sine wave.

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Re: What Sample Rate Do We Really Need?

Post by Shadowman82 » 31 Oct 2019 20:00

Rather than putting too much stock into a 100 year old math formula I'd say the sample rate is good enough when no human can tell the difference anymore . Studies have shown that some people can tell the difference between 16-bit/44.1khz and let's say 24-bit/96khz . Seeing that most masters today are somewhere in the 24-bit/ 96-192khz range it would be pointless to try and put out music at a higher resolution than that since you can't add what's not in the master . I also don't think you could hear a difference going higher .

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