[jcx]

 
Quote:

jcx: Thanks for the explanation! That matches what my lecturer said and what I've read in books. I should stop using the internet, seriously. Just confuses

 
 
Learning is Good - organized schooling can be very efficient - but practice, application to real world problems is where you really get the real appreciation for working theory
 
Signal theory and Electronic Engineering in general has some domains where the agreement between theory and practice is as good as it gets, orders of magnitude better than most Science, Engineering - try predicting effects, measuring to ppm in building construction
 
also it is one of the best represented on the web, with articles, even full university courses free on line
 
which makes it especially frustrating dealing with audiophoolish claims - at this point it has to be laziness or will-full ignorance when someone continues to spout the same nonsense after being pointed to the source information that the engineers that design the systems, equipment use, verify daily in the real world  

 

[xabu]

http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem
 
"In essence ..."
Don't know what "Trolling" got to do with it, but if such statemants make you feel better

 
I thought we're here  to discuss themes.
Obviously there are still different opinions.
 
If you read my statements thoroughly, you should know, that I agree that todays digital domain is superior in sound reproduction. BUT, and that was the whole idea from the beginning, perhaps it could be possible to come to an understanding without defamation of one or the other side.

 

[xnor]

There is no "common misconception regarding the Nyquist theorem". Not what you believe anyway.
 
If you don't understand it fully, then don't make such statements. Instead, ask pointed questions.
 
Otherwise, ... well you can see what happens

 

[xabu]

Quote:

There is no "common misconception regarding the Nyquist theorem". Not what you believe anyway.
 
If you don't understand it fully, then don't make such statements. Instead, ask pointed questions.
 
Otherwise, ... well you can see what happens

If somebody states that due to the Nyquist theorem it is possible to have a perfect (identical to the source) reconstruction in real world applications than this is a misconception in my understanding.
And you can read this simplification very often.
That it is nevertheless possible to have a sufficent reconstruction in real world applications because of many other facts is another thing.
 
Well if one wants to misunderstand one then one will.
 
I really don't see any problem.
 
I tried to state both sides of the existing opinions regarding the matter as a starting point without taking this or that side.
And I thought post no. 39 was a very good conclusion.
 
It's beyond me why to state part of a paragraph from the first post out of it's context and to start such an agressive follow up now.
 
The theme was Analog "versus" Digital. Mind the quotes !!!  (Kindergarten, really ...)
 

 

[JerryLove]

It is possible to have a digital version of an analog electrical waveform which, when converted back to analog and fed through a loudspeaker-style transducer, is indistinguishable to the human ear from the original analog waveform.
 
And that's all that really matters.

 

[DevanF]

So much information, I'll be reading these resources for days.
How many of you own a record player?

 

[brconner]

Actually the nyquist theory is perfectly sound. Assuming we had a perfect analog to digital converter with an infinite number of bits then we could perfectly store a signal as long as the max frequency is less than half the sampling rate. So the first problem is rounding from the ADC. Second problem is recreating the signal. Theoretically you can perfectly (yes perfectly) recreate the signal. Using a sinc function (http://en.wikipedia.org/wiki/Sinc_function) you can perfectly recreate the signal, including those points between samples that were never even stored. Digital to analog converters don't output sinc functions though so the output isn't perfect. So in practice you want the sampling rate to be at least 4 times the maximum frequency and preferably more.
 
So if we look at the standard 16-bit 44.1kHz we theoretically can reproduce a 22kHz sine wave, but in practice only frequencies up to 11kHz will be recreated near perfect. So all the main information in music is essentially perfectly stored. Most instruments fundamental and harmonic frequencies don't go above 6kHz! Now thats not all instruments obviously, cymbals for example can go as high as 16kHz. So CD quality isn't too bad actually. Obviously there is energy at higher frequencies, but most people don't notice it when its gone or have equipment that can reproduce it anyways. Obviously the higher the sampling rate and the higher number of bits will allow a more perfect representation and be closer to what we hear in real life.

 

[D. Lundberg]

 
Quote:

Assuming we had a perfect analog to digital converter with an infinite number of bits then we could perfectly store a signal as long as the max frequency is less than half the sampling rate. So the first problem is rounding from the ADC.

You don't need an infinite number of bits. The number of bits will just limit the dynamic range (as a result of the "rounding").
 
Quote:

Digital to analog converters don't output sinc functions though so the output isn't perfect. So in practice you want the sampling rate to be at least 4 times the maximum frequency and preferably more.

The converters use sinc pulses. Where did you get the idea that you would need to sample at 4x the maximum frequency?
 
Quote:

So if we look at the standard 16-bit 44.1kHz we theoretically can reproduce a 22kHz sine wave, but in practice only frequencies up to 11kHz will be recreated near perfect.

No, frequencies up to ~20-21KHz (depending on the filters) can be recreated "near perfect" (that is: with minimal distortion).
 
Quote:

Obviously the higher the sampling rate and the higher number of bits will allow a more perfect representation and be closer to what we hear in real life.

Not if the bandwidth (sample rate) and dynamic range (bit depth) already are sufficient.

 

[brconner]

To perfectly save the signal yes you would need an infinite number of bits. Rounding = Error. At what amount we can actually hear the difference I'm not sure, so of course theres a point were too many bits is just wasting memory. Same thing with sampling, there's a point where we won't notice a difference. The question from an engineering perspective is what that point is.
 
http://www.eetimes.com/design/embedded/4024581/Sampling-rates-for-analog-sensors
 
Most converters do not use sinc pulses. My mistake for saying a sinc function. The majority of DACs just use steps with some kind of filter to get rid of the higher frequencies created by the steps.
 
 
http://en.wikipedia.org/wiki/Digital-to-analog_converter
http://www.msbtech.com/support/How_DACs_Work.php
http://en.wikipedia.org/wiki/Sampling_(signal_processing)
 
Using a sinc function would take up too much time and memory. There are audio specific DACs that try to better reproduce the signals such as the delta-sigma method which tries to recreate those sinc pulses.
 
http://en.wikipedia.org/wiki/Sigma-delta_converter
 
Ideally if you take a 16-bit 44.1kHz sampling rate and put in a 22kHz signal you will get a perfect sine wave. In practice you need to sample faster than twice the frequency though. Try setting up an ADC and a DAC and you'll see that to recreate a signal with low distortion you'll need to sample much more than 2 times the frequency otherwise either your magnitude will be off or the phase will be off. This is something I have done and practiced. Lets say we have a 10kHz square wave, say something in electronica. Square waves are composed of a lot of sine waves. Take a look at this page
 
 

 
http://www.mathworks.com/products/matlab/demos.html?file=/products/demos/shipping/matlab/xfourier.html
 
If only the fundamental and third harmonics are used to make the square wave, it only sort of looks like a square wave. After adding the fifth harmonic it starts to look a lot better, but even still it doesn't look that great. So our square wave needs at least a 10kHz, 30kHz and 50kHz sine wave to make it look like a square wave. With our sampling rate, both the 30kHz and 50kHz have been cut out or worse aliasing will occur (http://en.wikipedia.org/wiki/Aliasing). Assuming those harmonics were just filtered the output is just going to be a 10kHz sine wave. Doesn't seem like our system is accurately depicting what was put in to begin with. I said at least 4 times faster, but a lot systems will do 10 times or more. Even at four times (about our 44.1kHZ) this square is not accurately recreated. At ten times the frequency we'll get pretty close to that actual square wave we put in.

 

[jcx]

why do people always ignore the fact that we're talking about real world "measurements" or "information channels" - we are not trying to reproduce some Platonic Ideal "infinite resoution" signal - the venue, the microphone, preamp any part of the signal chain is limited by noise and has limited bandwidth - this means any signal is inherently "uncertain" - no 2 SOTA recording processes, identical microphones or excellent preamps connected to the same microphone will give exactly the the same V at the instant in time
 
there is not "infinite resolution" in any real world signal - so any real world "analog" signal can be represented as well as it can be known by any technology by a finite number of bits

 

[D. Lundberg]

     Quote:

To perfectly save the signal yes you would need an infinite number of bits. Rounding = Error. At what amount we can actually hear the difference I'm not sure, so of course theres a point were too many bits is just wasting memory. Same thing with sampling, there's a point where we won't notice a difference. The question from an engineering perspective is what that point is.

 
 
 
 
 

The errors from rounding will represent white noise (that is: the errors will not be correlated to the signal) in a properly dithered signal, and the amount of noise determines the dynamic range.
 
* The bit depth determines the amount of quantization steps (amplitude values).
* The amount of quantization steps determines the amount of quantization error.
* The amount of quantization error determines the amount of quantization noise.
* The amount of quantization noise determines the level of the noise floor.
* The level of the noise floor determines the dynamic range.
 
The dynamic range (and thus the number of bits) needed is determined by the signal, the playback/recording environment, playback amplitude (SPL) and the limits of the human auditory system.
 
Quote:

Ideally if you take a 16-bit 44.1kHz sampling rate and put in a 22kHz signal you will get a perfect sine wave. In practice you need to sample faster than twice the frequency though.

That's because you'll need some room for the filter. The signal must be fully attenuated at 22.05kHz, so a 22kHz sine wave will be in the transition band of the filter.
 
Quote:

If only the fundamental and third harmonics are used to make the square wave, it only sort of looks like a square wave. After adding the fifth harmonic it starts to look a lot better, but even still it doesn't look that great. So our square wave needs at least a 10kHz, 30kHz and 50kHz sine wave to make it look like a square wave. With our sampling rate, both the 30kHz and 50kHz have been cut out or worse aliasing will occur (http://en.wikipedia.org/wiki/Aliasing). Assuming those harmonics were just filtered the output is just going to be a 10kHz sine wave.

A 10kHz sine wave is what it should be if the system is properly band limited. And more important: that's what it will sound like, because the 10kHz fundamental is the only tone that's audible to humans.
 
Quote:

Doesn't seem like our system is accurately depicting what was put in to begin with.

It's accurately depicting a band limited version of the signal, and represents the part of the signal that is audible to humans.
There is no reason whatsoever to reproduce the ultrasonic frequency content of a 10kHz square wave.

 

[brconner]

I really like how you connected the bit depth to the dynamic range. Thats probably the clearest description of them I've seen. 
 
Thats correct about the square wave the system should only output that one sine wave, but if I'm observing signals I'd rather get any kind of signal (sine, square, triangle, etc) at it's fundamental frequency than just the sine waves. Also if we go back to the original post we're trying to compare analog systems and digital systems. The example I gave is one that shows the problems you can run into if you don't sample fast enough. I admit a 10kHz square wave is an extreme example since your right in that the only frequency we should hear is the 10kHz fundamental sine wave.

 

[D. Lundberg]

 
Quote:

Thats correct about the square wave the system should only output that one sine wave, but if I'm observing signals I'd rather get any kind of signal (sine, square, triangle, etc) at it's fundamental frequency than just the sine waves.

Complex waveforms don't exist at a specific frequency, they are a continuum. Observe the spectrograph plot of the signal if you really want to understand what's going on.
And shouldn't the focus be on the parts of the signal humans actually can hear?

 

[brconner]

 
As I stated in my earlier post a square wave is an infinite number of sine waves added together. Triangle wave, same thing different harmonics with different amplitudes. I already know what I would see on a spectrograph plot. I work with much more than audio so many times I'm not concerned with what can be heard and want to make sure what I'm measuring is what is actually there.
 
Of course for audio all we need to worry about is what can be heard. Whenever I've compared my various music formats I've found vinyl to sound the best, but I'm sure there's a strong mental effect influencing that since mathematically I shouldn't be able to hear much of a difference. I have wondered for awhile though if our hearing can have an alias effect like what you would see on an ADC without filtering. Ultimately the sound we hear is converted back into some electrical signal that goes to our brain so maybe we have the same problem that digital sampling can have? 

 

[BlackbeardBen]

Quote:

 
As I stated in my earlier post a square wave is an infinite number of sine waves added together. Triangle wave, same thing different harmonics with different amplitudes. I already know what I would see on a spectrograph plot. I work with much more than audio so many times I'm not concerned with what can be heard and want to make sure what I'm measuring is what is actually there.
 
Of course for audio all we need to worry about is what can be heard. Whenever I've compared my various music formats I've found vinyl to sound the best, but I'm sure there's a strong mental effect influencing that since mathematically I shouldn't be able to hear much of a difference. I have wondered for awhile though if our hearing can have an alias effect like what you would see on an ADC without filtering. Ultimately the sound we hear is converted back into some electrical signal that goes to our brain so maybe we have the same problem that digital sampling can have? 

I think that's where you tripped up everyone else.  Since square/sawtooth/triangle waves are infinite series of sine waves, and the Nyquist-Shannon sampling theorem applies to the sine wave sense of the signals, we of course know that the sum of those non-finite sine wave series cannot be reproduced with low levels of distortion at a sampling rate only twice the fundamental frequency.
 
But as you pointed out, that doesn't matter when those harmonics are above human hearing thresholds in frequency (or below the threshold in volume compared to the total signal).  If you're talking signals processing beyond just audio - of course, that's an entirely different animal.
 
 
 
 
About vinyl vs. digital - well, I'd say that if we're comparing ideally processed media of the same recording in each domain (i.e. the digital media isn't manipulated to sound like the analog one), there may indeed (if not should) be audible differences.  Stereo separation, for one.  Additional harmonic distortion, maybe, but it may also be desirable.  Flutter/wow; perhaps not audibly with the best setups.  Pops and clicks on LPs to be sure, as well as a possibly audible higher general noise floor.
 
But this is what should be important:  Is it possible, and what does it take to reproduce that LP/tape in the digital domain so that when it is played back it is indistinguishable from the original to humans?
 
That's something we don't explicitly know the answer to yet.  However, I'd put money on Redbook CD at 16/44.1 being sufficient for replicating an LP or tape.  That's given that the lower noise floor/higher dynamic range (the same thing) is the only proven audible advantage of higher bit rate recordings, and that advantage is more or less unneeded when the noise floor of the analog recordings is higher than that of basic Redbook.  As for higher sampling rates, unless we're listening to sine wave test tones, the audibility of 20 kHz + tones for even the best trained ears during actual music playback is more or less unfounded; considering the demonstrated transparency of LAME V0 mp3s (on all but the few killer samples) that basically throw out everything above 16 kHz or so.