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Understanding Upsampling/Interpolation

Lambda

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Actually, there are no assumptions. It's a proven theorem, mathematically.
Sorry maybe "assumptions" is the wrong word. of cause its true and proven!
I meant to say conditions must be establishes. for example the signal must have limited bandwidth.

And "perfect" reconstruction of this band limited signal is only possible if amplitude can be sampled perfectly.
 

j_j

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Sorry maybe "assumptions" is the wrong word. of cause its true and proven!
I meant to say conditions must be establishes. for example the signal must have limited bandwidth.

And "perfect" reconstruction of this band limited signal is only possible if amplitude can be sampled perfectly.

And, now, we can take a 24 bit recording, which is actually usually 21 or 22 bits, overdithered, and compare that to tape, vinyl, wire recorder, what-have you, and which has more noise?

Remember that a dithered quantizer is pure additive noise.
 

pma

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And, now, we can take a 24 bit recording, which is actually usually 21 or 22 bits, overdithered, and compare that to tape, vinyl, wire recorder, what-have you, and which has more noise?

In case that the recording does not have extra high dynamic range (and the volume knob is not raised during low level passages) and very low noise microphone path, the tape S/N would be enough and vinyl as well, if we forget possible surface clicks, IMO.
 

Lambda

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Not trying make an argument against discrete time sampling...
I'm just saying the real world is not perfect.
Noise is everywhere and all else being equal the higher the sampling rate the lower the in band noise.

How mush SNR is needed is a whole nother question.
 

j_j

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Not trying make an argument against discrete time sampling...
I'm just saying the real world is not perfect.
Noise is everywhere and all else being equal the higher the sampling rate the lower the in band noise.

How mush SNR is needed is a whole nother question.


How much? Much, much less than 22 or 23 bits, is the answer. The noise level of the ATMOSPHERE comes into play here. Really.

The noise level of the atmosphere AT THE EARDRUM, 20-20K is on the order of 6dB SPL to 8dB SPL. There is no point in being lower than that. 20 bits above that is 120dB above that, or 126dB, which is above any safe listening level at all. If we want to go to 24 bits (not that I think any convertor out there does that), that's 144+6 = 150dB which is:

1) Well above the linear level for atmosphere transmission
and
2) Above the "instant damage to hearing" level.

So. Really. 20 bits is enough for any sane capture, given that the noise level in a quiet listening room is in the 40dB SPL range usually to start with. There's a thread on this somewhere around here.
 

Lambda

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There is no point in being lower than that. 20 bits above that is 120dB above that, or 126dB,
~130dB Peak at 20Hz is far from "instant damage to hearing" level .
And the ideal perfect DAC should have sufficient headroom so its possible to boost some frequency's in DSP/EQ and/or Linearization with predistortion
+ some extra headroom so the user don't have to worry about gain staging and volume control at all


But as i said this is a whole another question and not about upsampling/interpolation.
 

j_j

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~130dB Peak at 20Hz is far from "instant damage to hearing" level .

I'm afraid we'll have to disagree on that. Please look at the cochlear mechanisms and where low frequencies are detected.

I'm also curious as to how 150dB became 130dB.
 

Lambda

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I'm also curious as to how 150dB became 130dB.
126dB became 130dB.
At sufficiently low frequency's and for short period es of time... Maybe not absolute save but so is smoking and some do it.

depending on regulations the allowed exposure is very different
http://www.sengpielaudio.com/PermissibleExposureTime.html
peak noise limit value is 140 dB measured as the instantaneous C-weighted

yeah 150dB is maybe stretching it.
But normal audio DACs have a hard time even going to 126dB dynamic.

https://www.hearingreview.com/inside-hearing/research/know-loud-balloons-can
on the other hand pooing a balloon is over 150dB and i think we have all done it...
 

j_j

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Ok, now let's consider your speakers. What's their efficiency, and what's the peak output from your amp?

Seriously. Let's look at all of this in context. You only get one set of inner hair cells. Be nice to them.
 

Lambda

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Ok, now let's consider your speakers. What's their efficiency, and what's the peak output from your amp?
There are Balanced Armature IEM abel to reach insane sound pressure levels
I don't know why we have this discussion. :)
Sure its not a good idea. regularly listen to this volume levels!

I'm just saying normal DACs don't reach the SNR ears can deal with.
maybe they are "good enough" but this is just not my definition of perfect.

No, the spectrum due to brownian motion at the ear drum is very close to pure white.
sure about this?
also known as Brown noise or red noise, is the kind of signal noise produced by Brownian motion, hence its alternative name of random walk noise.
https://en.wikipedia.org/wiki/Brownian_noise
 

j_j

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PeteL

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That is true. Upsampling allows a more gentle filter to be used since there is so much ultrasonic bandwidth to sacrifice. This crude picture shows the concept:

filters.png


Gentle filters have less artifacts in the 20 Khz range that we care about.

Now, whether this is an audible problem is another matter. :)
And your view on the matter, is it audible?
 
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