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[Dumdum]

3 years late with this comment, but 96khz has nothing to do with frequency response. It refers to sampling frequency.

Which directly influences maximum freq it can reproduce… so it is directly related to freq response as he states

 

[ahofer]

3 years late with this comment, but 96khz has nothing to do with frequency response. It refers to sampling frequency.

But, to be fair, the concepts are related, and the original 44Khz threshold was designed at 2X the upper threshold of human hearing. Higher sampling rates are required to accurately reproduce high frequencies and help avoid filter effects invading the audible spectrum.

 

[rarewolf]

3 years late with this comment, but 96khz has nothing to do with frequency response. It refers to sampling frequency.

But sampling does have something to do with frequency and tonal accuracy… so it does have something to do with response, generally speaking…

 

[jareinertson]

Which directly influences maximum freq it can reproduce… so it is directly related to freq response as he states

Agreed, however unless the initial recording included frequencies above 22k then the sampling frequency “should” not have an effect on audible playback…

 

[jareinertson]

But sampling does have something to do with frequency and tonal accuracy… so it does have something to do with response, generally speaking…

Agreed

 

[morillon]

44k/*..BP 22khz
48k/*.....24khz
96k/*....48khz
Etc

 

[rarewolf]

Agreed, however unless the initial recording included frequencies above 22k then the sampling frequency “should” not have an effect on audible playback…

The Nyquist–Shannon sampling theorem that would imply that all you need is to sample waveform twice isn’t perfect. It only states that if you sample many waveforms twice that you can trust statistical error analysis. The fact remains that if you can afford to sample a waveform many times its measurement will be even more accurate (i.e., less error). With respect to digital storage, the keyword here of course is “afford”…

 

[antcollinet]

3 years late with this comment, but 96khz has nothing to do with frequency response. It refers to sampling frequency.

And what sampling frequency gets you is bandwidth. 44.1kHz will get you just over 20kHz bandwidth. 96kHz will get. you just under 48kHz bandwidth.

Anything over 48kHz sampling frequency (22kHz bandwidth - even allowing for filter rolloff) is overkill. Not needed - of no audible benefit. Humans can't hear it..

 

[antcollinet]

The Nyquist–Shannon sampling theorem that would imply that all you need is to sample waveform twice isn’t perfect. It only states that if you sample many waveforms twice that you can trust statistical error analysis. The fact remains that if you can afford to sample a waveform many times its measurement will be even more accurate (i.e., less error). With respect to digital storage, the keyword here of course is “afford”…

No not so. If you sample at half the maximum frequency in the band limited signal - that signal can be reconstructed perfectly. This is what Nyquist-Shannon demonstrates mathematically.


It is time for Monty, where he demonstrates exactly this practically - no maths knowledge needed. For this specific topic you need 17:21 - but if you want to get a good grounding in digital audio rather than myths that most people believe, watch the whole thing. Then watch it again, and again. I did.

 

[rarewolf]

No not so. If you sample at half the maximum frequency in the band limited signal - that signal can be reconstructed perfectly. This is what Nyquist-Shannon demonstrates mathematically.

…

Depending on Nyquist is never “perfect”. Possibly near “perfect” for lower and mid frequencies, but frequencies over 8kHz would be heavily staircased, but audibly recognizable.

I worked with, and taught, applied sampling frequencies for over 30 years

 

[morillon]

But that impacts the impulse response too, doesn't it? ;-)

 

[antcollinet]

Depending on Nyquist is never “perfect”. Possibly near “perfect” for lower and mid frequencies, but frequencies over 8kHz would be heavily staircased, but audibly recognizable.

I worked with, and taught, applied sampling frequencies for over 30 years

Please - Watch the video. Only NOS filterless DACS (broken by design, and there are almost none of them) create stair steps. Any oversampling DAC with a proper reconstruction filter has no stair steps, and can - even at 44.1kHz perfectly reconstruct a 20khHz sine wave and any other signal that is band limited to 20kHz or less.

Watch the whole thing - but the stair steps myth is demonstrated to be nonsense from about 3:38

I worked with, and taught, applied sampling frequencies for over 30 years

Really? Then if you taught "stair steps" you were badly letting down your students.

 

[rarewolf]

Please - Watch the video. …

Only NOS filterless DACS (broken by design, and there are almost none of them) create stair steps. Any oversampling DAC with a proper reconstruction filter has no stair steps, and can - even at 44.1kHz perfectly reconstruct a 20khHz sine wave and any other signal that is band limited to 20kHz or less.

Watch the whole thing - but the stair steps myth is demonstrated to be nonsense from about 3:38
…

What he described and demonstrated was pretty easy to accomplish with a pure sine wave, and with corrections that “assume” a perfect sine wave.

Now, music can argued to be nothing other than a collection of sine waves at various frequencies… but… it is a continuous mixture of nearly an infinite number of different sine waves that define time structures of an infinite number of different shapes. For example, consider a mixture of sawtooths, or a mixture of square waves at different frequencies. Exactly how are you going to draw the leading or trailing edges accurately by sampling only at twice the highest frequency expected and assuming pure sine waves?

As scientists, we would never create data where no data exists. It would be called a “projection”, and qualifying a result as “accurate” or “precise” would be laughable. Admittedly, throwing “corrected” digitized music at consumers isn’t against any laws, and can be gotten away with because it’s “near perfect”, but do not laugh at audiophile purists who only want to listen to “uncorrected” digital data who know higher rate samplings represent reality more accurately based on higher precision… even if we cannot A/B the difference… it happens to be who we are.

#jussayin

 

[kyuu]

I really hope rarewolf is lying about having taught a class about "applied sampling frequencies" as they plainly don't understand the topic very well.

 

[krabapple]

What he described and demonstrated was pretty easy to accomplish with a pure sine wave, and with corrections that “assume” a perfect sine wave.

Now, music can argued to be nothing other than a collection of sine waves at various frequencies… but… it is a continuous mixture of nearly an infinite number of different sine waves that define time structures of an infinite number of different shapes. For example, consider a mixture of sawtooths, or a mixture of square waves at different frequencies. Exactly how are you going to draw the leading or trailing edges accurately by sampling only at twice the highest frequency expected and assuming pure sine waves?

As scientists, we would never create data where no data exists. It would be called a “projection”, and qualifying a result as “accurate” or “precise” would be laughable. Admittedly, throwing “corrected” digitized music at consumers isn’t against any laws, and can be gotten away with because it’s “near perfect”, but do not laugh at audiophile purists who only want to listen to “uncorrected” digital data who know higher rate samplings represent reality more accurately based on higher precision… even if we cannot A/B the difference… it happens to be who we are.

#jussayin

Music isn't a special case of audio signal from the perspective of audio sampling.

Your promotion of cases that don't reflect the physical world -- where everything has bandwidth limits, even 'square' waves, and of course, human hearing itself -- and your dismissal of interpolation and reconstruction -- which make digital audio sampling actually 'work' -- means you seriously should not ever be teaching the subject.

 

[antcollinet]

What he described and demonstrated was pretty easy to accomplish with a pure sine wave, and with corrections that “assume” a perfect sine wave.

Now, music can argued to be nothing other than a collection of sine waves at various frequencies… but… it is a continuous mixture of nearly an infinite number of different sine waves that define time structures of an infinite number of different shapes. For example, consider a mixture of sawtooths, or a mixture of square waves at different frequencies. Exactly how are you going to draw the leading or trailing edges accurately by sampling only at twice the highest frequency expected and assuming pure sine waves?

As scientists, we would never create data where no data exists. It would be called a “projection”, and qualifying a result as “accurate” or “precise” would be laughable. Admittedly, throwing “corrected” digitized music at consumers isn’t against any laws, and can be gotten away with because it’s “near perfect”, but do not laugh at audiophile purists who only want to listen to “uncorrected” digital data who know higher rate samplings represent reality more accurately based on higher precision… even if we cannot A/B the difference… it happens to be who we are.

#jussayin

Frankly this is not even up for debate. It is like a teacher of geography debating the flatness vs sphericalness of the earth. The sampling theorem was proven decades ago - and what it mathematically proves is any sample rate greater than double of the bandwidth limit of a signal stores enough information for perfect reconstruction of *any* signal within that band limit (music included). This has been fully understood for decades, ADCs and DACs (And all digital signal processing - whether audio or anything else) have used this maths for decades - and simple tests can show that it works, no matter how complex the (in band) signal. If you are still teaching this stuff you have a duty to your students to do a lot of reading, learning and understanding between now and your next lesson.

A good place to start would be to watch all the linked video - while putting out of your mind the thought that he (or we) are trying to trick you. Then watch it again - and again, until you fully understand what it is *demonstrating* to you.

From wikipedea (my bold)

Nyquist–Shannon sampling theorem - Wikipedia

en.wikipedia.org

The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.

Intuitively we expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result depends on the density (or sample rate) of the original samples. The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity for the class of functions that are band-limited to a given bandwidth, such that no actual information is lost in the sampling process. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions. The theorem also leads to a formula for perfectly reconstructing the original continuous-time function from the samples.

By the way - neither sawtooth waveforms, nor sqare waves are band limited. They both have infinite band width. When you band limit them - the limiting "rounds off" the corners with gibbs phenomena - that allows the sample rate to capture sufficient information to perfectly reproduce them.

 

[antcollinet]

As scientists, we would never create data where no data exists.

And here is my last word to you. An analogy that might help you.

Let’s say you were transmitting information about two-dimensional shapes to a remote location. If the shapes could be literally anything, then you would have to transmit infinite information to fully accurately define the shape. An infinite sequence of xy points around the edge of the shape.

But let’s say we only wanted to transmit circles. Then for each circle we would only need two pieces of informatioin. The coordinates of the centre, and the coordinates of any point on the circumference. With those two pieces of information, you can perfectly draw that circle. A scientist might say that you can't put data around the circumference where no data exists - but you would know better. Those two pieces of information are sufficient to capture all the information about the circle. We don’t need to plot an infinite sequence of coordinates around the circumference to define it.

Limiting the shapes to circles is the equivalent of band limiting in digital audio or DSP. It allows us to perfectly draw the waveform - even though we only have two points for each cycle of the highest frequency in the signal. We know what it looks like because we know it has no higher frequencies in it.