44kHz sampling freq. gives 1 sample per halfwave for 20kHz sine ?

[darkfenriz]

...
There is a reason why the CD format was chosen to use 44.1Khz, not just 40Khz, and it is to be able to avoid some of those practical problems to implement the math world solutions.
....

what's the reason?
it heard there were two reasons:
-to make the rate compatibile with one yet existing mechanical engine of Philips
-to make the rate not compatibile with digital cassettes

 

[Euphase]

You can only reconstruct the part of the signal that is below half the sampling freq

If you sample a perfect 20 khz square wave using a 40 khz sampling freq, you will get a nice 20 khz sine wave (the fundemental freq) after the A/D converter and filter.

\Jens

That's no different than what I wrote, which was:

Actually, I believe it is different than what I wrote. When the signal is 20Khz square wave, it is not band limited to 20Khz, the components that make up that 20Khz square wave that is above 20Khz will be folded back on to the 0-20Khz range, and one will end up with something different than a 20Khz sine wave. Hence the signal needs to be filtered first. I am not an expert on signal processing, just learning things as I go, but this is how I see it working.

 

[Bernhard]

For me it is clear now, the limitation of the bandwith does not allow anything else than a sine at 20 kHz.
But doesn`t that asks for a high order filter ?
If we want to get a low distortion sine from a 20k "something that looks like a square directly on the DAC out", we need to filter out the content above 20 kHz as steep as we can.
Or can we say that a 10 kHz signal which is distorted because of K3 ( 30kHz ) sounds clean because we can not hear the 30kHz and thus can not hear the distortion ???

 

[Euphase]

what's the reason?
it heard there were two reasons:
-to make the rate compatibile with one yet existing mechanical engine of Philips
-to make the rate not compatibile with digital cassettes

I found some info here

http://www.lacoj.com/resources/CD Encoding.htm#S2-35

My original point was that, if theory and math didn't encounter any problems when taken into real world, a sampling of 40Khz makes more sense, it would lower the amount of data needed to be stored, require slower circuits etc. But reality requires a higher sampling than the ideal lower sampling frequency, mostly because you can't make an anolog ideal brickwall 20Khz LP filter.

I am not saying a higher sampling rate will not be superior, all I am saying is some of the posts that object the current CD rate is not actually pointing to the real problems.

 

[Euphase]

For me it is clear now, the limitation of the bandwith does not allow anything else than a sine at 20 kHz.
But doesn`t that asks for a high order filter ?

Yes, it does ask for a high order filter, which cause phase distortion, but is it auiable at those frequencies is another debate I guess.

Or can we say that a 10 kHz signal which is distorted because of K3 ( 30kHz ) sounds clean because we can not hear the 30kHz and thus can not hear the distortion ???

Yeap, that's right But it doesn't mean that if a system is causing K3 at 10Khz is harmless. Because where there is harmonic distortion, it is very likely that it will cause intermodulation distortion. So the nonlinearity that causes the K3 at 10Khz, is very likely to cause some intermodulation distortion between a say 1Khz and 10Khz signal, and end up putting out some distortion products at audiable range below 20Khz

 

[wistily]

You can only reconstruct the part of the signal that is below half the sampling freq

If you sample a perfect 20 khz square wave using a 40 khz sampling freq, you will get a nice 20 khz sine wave (the fundemental freq) after the A/D converter and filter.

And your ear... can only listen to the 20khz sine wave (or perhaps you are a bat or something like that ), so all is fine.

 

[SY]

Well, there have been experiments that show that the difference between 16 and 24bit is audible, and I think I also remember seeing some showing the same for the difference between even 44.1 and 48kHz, so it seems reasonable to assume that converting to/from 16/44.1 will be audible compared to the original analogue.

Can you give me a citation for these experiments?

 

[marconist]

I really don't understand what you are trying to say.

There is a reason why the CD format was chosen to use 44.1Khz, not just 40Khz, and it is to be able to avoid some of those practical problems to implement the math world solutions. A higher sampling rate will make things easier, but let's not mix apples with oranges.

You forget that in an audible sound system there are no sine waves .... so it is not really interesting that I can conclude (mathematically) that indeed all signal forms are deductable to sine waves.
If you analyse a audible analog sound wave from, let's say 12 kHz- 20 kHz you find all kinds of waveforms, even sine waves.
The overtones (2nd harms) are however mostly non-sine, but they do determine the sound colouration ic. determine whether a sound is recognized as coming from a voice or an organ.
The 3rd harmonics are of course also part of the colouration, but they are interpreted by our hearing as "harsh".

To output hifi we must be able to reconstruct "funny" waveforms up to some 20 kHz (assuming you are a male under 40 ) otherwise the sound is just makebelieve like in AM-radio.

There is nothing wrong with the mathematical side, as long as you remember that we humans are not listening to sine waves, but to complex sound waveforms.

The 44.1 was chosen for marketing reasons; just to promote 20 kHz as upper limit. Indeed the filtering is the problem why the sampling rate is not 40 kHz.
A higher sampling frequency was not feasable due to the cost of electronics components in those days.

 

[JensRasmussen]

And your ear... can only listen to the 20khz sine wave (or perhaps you are a bat or something like that ), so all is fine.

I only told you how sampling works... there might be sampled systems where signals are needed that have a higher freq than 20 khz.... I think ADSL DSPs have a higher upper freq limit

\Jens

 

[Euphase]

If you analyse a audible analog sound wave from, let's say 12 kHz- 20 kHz you find all kinds of waveforms, even sine waves.

A sound wave that is band limited to 12Khz and 20Khz, means it is made up of linear combinations, i.e. sum of various amplitude and phase of everlasting sine waves with frequencies of ONLY 12Khz to 20Khz. That's it. It sounds to me you are not clear on what is a frequency decomposition, or the frequency spectrum of a wave form.

The overtones (2nd harms) are however mostly non-sine, but they do determine the sound colouration ic. determine whether a sound is recognized as coming from a voice or an organ.

Saying overtones are mostly non-sine doesn't make any sense.

To output hifi we must be able to reconstruct "funny" waveforms up to some 20 kHz (assuming you are a male under 40 )

See above again. A waveform limited by 20Khz can only contain a 20Khz sine wave component in its spectrum. It can't have a 40Khz component for instance, if it had, then it would have a bandlimit at least 40Khz. A frequency spectrum is made up of everlasting sinosiddial waves only.

There is nothing wrong with the mathematical side, as long as you remember that we humans are not listening to sine waves, but to complex sound waveforms.

No offense, but I think you really need to spend some time better understanding the Fourier Transformation, Fourier Series, superposition etc.

The 44.1 was chosen for marketing reasons; just to promote 20 kHz as upper limit.

You are contradicting yourself here, above you said human's hearing is limited with 20Khz, and now you are saying it is just a promoted limit

 

[real]

To output hifi we must be able to reconstruct "funny" waveforms up to some 20 kHz (assuming you are a male under 40 ) otherwise the sound is just makebelieve like in AM-radio.

You are confusing yourself with what we can hear - these 'funny' waveforms cycling at 20kHz can be decomposed with 20kHz SINE waves + higher frequency SINE waves. You can only hear the 20kHz SINE wave component of the signal - for example, a 20kHz square wave will sound exactly the same as a 20kHz sine wave to us, since we do not hear the higher order harmonics of the square wave (if you can still hear up to 20kHz, that is - perhaps a better example would be 10kHz square/sine waves).

Thus, all frequency content above 20kHz was deemed not necessary, and is filtered out of the signal. Whilst this will mean that the reconstructed waveform will be different from the original, it will still have the same 0-20kHz frequency content, i.e. the stuff we hear.

If you are still in doubt about this, I suggest you read a textbook on Fourier transforms, sampling theorems and the like.

Chris.

Edit: Whoops, Euphase just posted on this, but maybe this provides a different view

 

[marconist]

A sound wave that is band limited to 12Khz and 20Khz, means it is made up of linear combinations, i.e. sum of various amplitude and phase of everlasting sine waves with frequencies of ONLY 12Khz to 20Khz. That's it. It sounds to me you are not clear on what is a frequency decomposition, or the frequency spectrum of a wave form.
Just an example ...... I assume you know as well that the base frequencies in musical and voice waves do not exceed some 5kHz.

Saying overtones are mostly non-sine doesn't make any sense.
Not if you listen to sine waves only.

See above again. A waveform limited by 20Khz can only contain a 20Khz sine wave component in its spectrum. It can't have a 40Khz component for instance, if it had, then it would have a bandlimit at least 40Khz. A frequency spectrum is made up of everlasting sinosiddial waves only.
Nice statement, true as well.

No offense, but I think you really need to spend some time better understanding the Fourier Transformation, Fourier Series, superposition etc.
I must admit, its many years ago that I played around with fourier-analyzers at my job (HP)

You are contradicting yourself here, above you said human's hearing is limited with 20Khz, and now you are saying it is just a promoted limit
What contradiction is there in a practical limit?

The problem with hearing is that not all people hear the same. That's why Fletcher-Munson could not decide over ca. 15 kHz.
Some people that cannot hear over 15 kHz, still can hear "a difference" when you take a musical signal that extends over 25 kHz, let them listen to it and then limit it at 17 kHz (at -6 dB/oct).
Why? I don't know ..... maybe we don't hear a mix of sine waves?

 

[jan.didden]

hallo guys
it's been a good read..
one more thing to discuss here I think. The higher sampling rate makes an ADC less prone to analog anti-aliasing filter imperfection. Not only wide-band noise of filter aliases, but also harminic distortion and possibly products of HF instability. Don't forget they are made of op-amps and quite complex in terms of phase response within high-feedback loop!!!
It could be useful to use high sampling rate for ADC.

for DAC it is the same thing again-the 'stairway' signal from adc has wide bandwidth and HF components can easily intermodulate in interpolation filter. Actually we don't know how signals intermodulate in op-amp based filter. Op-amps are measured for IM with non-reactive impedances within feedback.

What do you think?

best regards

I agree that one (or maybe the only) reason for higher sampling rate is that the filtering becomes much easier. In theory, if you go high enough in sampling (786kHz, anyone) you can get away with just a passive filter, and it is clear that that may sound much, ehh, clearer than a steep, phaseshift-loaded opamp filter just above 20kHz. But there is nothing in the higher sampling rate that is of advantage to the sampling process itself: 44.1 kHz is perfectly able to sample and reconstruct 20kHz, thank you.

Jan Didden

 

[wistily]

You can only hear the 20kHz SINE wave component of the signal - for example, a 20kHz square wave will sound exactly the same as a 20kHz sine wave to us, since we do not hear the higher order harmonics of the square wave (if you can still hear up to 20kHz, that is - perhaps a better example would be 10kHz square/sine waves).

Hello.
On that fact, someone once said to me that there wasn't any proof that the human ear was behaving like a low pass filter.
Have you references on that topic ?

 

[real]

Hello.
On that fact, someone once said to me that there wasn't any proof that the human ear was behaving like a low pass filter.
Have you references on that topic ?

Hi wistily,

I do not know any references to that. However, I don't see any lack of proof - we can't hear above 20kHz - I have tried, couldn't hear above ~18kHz. Surely this constitutes a low pass filter.

I am no expert, but maybe the ear itself is not the one performing any low pass filtering, perhaps it is in the brain. However, I don't think this is the case - I suspect it is the cochlea (the 'snail shell' part of the inner ear) which results in any band limiting of our hearing. Someone please correct me on this.

Chris.

 

[Euphase]

The problem with hearing is that not all people hear the same. That's why Fletcher-Munson could not decide over ca. 15 kHz.
Some people that cannot hear over 15 kHz, still can hear "a difference" when you take a musical signal that extends over 25 kHz, let them listen to it and then limit it at 17 kHz (at -6 dB/oct).
Why? I don't know ..... maybe we don't hear a mix of sine waves?

I will repeat again, from your posts I really think you don't have a good understanding of what a frequency spectrum of a signal is, how time domain and frequency domain relate etc. In this electronic form of communication, it is possible that I might have misunderstood you also, but others who have been reading your posts might be misunderstanding the same way I did. That's why I wanted to point out the things in your posts that are not correct the way they are written or the way I read them

As for hearing above 20Khz, or being able to discern the difference between a signal that contains components above 20Khz and one doesn't, do you have any references that have been studied and experimented in a well defined way? I am tired of hearing anectodal, subjective statements, ranging from people even hear better with green marked CDs to other things.

I heard about an experiment where they looked at brain activity which showed some extra activity when frequency components above 20Khz existed, but I also heard that that experiment wasn't repeatable also.

 

[marconist]

As for hearing above 20Khz, or being able to discern the difference between a signal that contains components above 20Khz and one doesn't, do you have any references that have been studied and experimented in a well defined way?

You can do that yourself: take a headphone, determine your upper hearing frequency (sine), run a piece of music with components well above your max hearing and then use an equalizer to cut off just above your max hearing.


I am tired of hearing anectodal, subjective statements, ranging from people even hear better with green marked CDs to other things.

I recognize that, I used to fight the "vinyl guys" a long time .... No, I did not change to the camp of the people that hear differences in power cords.

Slightly off topic, but may be interesting to read about the (conceptial?) differences in theory and practise:
http://www.ucs.louisiana.edu/~brm2286/sampling.pdf

 

[scott wurcer]

You may want to check out the writings of James Boyk: http://www.performancerecordings.com/writings.html
Cal Tech seems to still host his paper on instruments that go up to 100KHz.

 

[Euphase]

You can do that yourself: take a headphone, determine your upper hearing frequency (sine), run a piece of music with components well above your max hearing and then use an equalizer to cut off just above your max hearing.

Problem with that is, the nonlinear components used (at least the speakers are very nonlinear) will cause intermodulation which will cause some extra components to fall below 20Khz, which will invalidate the test. And also LP filter will cause linear distortion (phase and some amplitude). There are lots of pitfalls...

Slightly off topic, but may be interesting to read about the (conceptial?) differences in theory and practise:
http://www.ucs.louisiana.edu/~brm2286/sampling.pdf

I will check that out.

I have just found this one, but haven't read it completely, talks about an experiment on brain activity and high frequency content.

http://jn.physiology.org/cgi/reprint/83/6/3548.pdf

 

[scott wurcer]

Slightly off topic, but may be interesting to read about the (conceptial?) differences in theory and practise:
http://www.ucs.louisiana.edu/~brm2286/sampling.pdf

That paper is a bad example. It's was reviewed for a biologists conference and doesn't contain any theoretical analysis. A rigorous analysis of his signals would probably point to most of the conclusions, most importantly that there was information at higher frequencies than they thought. Transient signals tend to spead out in frequency content.