John and Undertow, you are attempting to explain the finer points of sampling theory to someone who only possesses an intuitive understanding of the subject. Recommend a good book on the subject and invite him to come back in a year to discuss it further.

You're 100% right.

bitflipper


"On two occasions, I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able to rightly apprehend the kind of confusion of ideas that could provoke such a question."
- Charles Babbage

John and Undertow, you are attempting to explain the finer points of sampling theory to someone who only possesses an intuitive understanding of the subject. Recommend a good book on the subject and invite him to come back in a year to discuss it further.

bitflipper maybe it's not me missing the finner points. I have stated that sampling higher than the nyquist rate on audio signals will produce a better reconstructed signal. I have made no claim that it can be heard. I have made no point of argument that one should do so. 

UnderTow

rabeach


To dismiss outright that a more accurately reconstructed signal has no value because you can't hear it in double blind studies with current technology is IMHO short sided at best. Obviously a more accurately reconstructed signal can be quantified and perceived just not with your auditory sensory receptors using current technology.

You don't get it: The audible signal will not be more accurately reconstructed by increasing the bandwidth.

Again, you are clearly out of your depth with this topic.

UnderTow

what is this post in reference to?

I have stated that sampling higher than the nyquist rate on audio signals will produce a better reconstructed signal

I am saying that isn't so. It wont create any better signal. Is that clear enough?

I have made no claim that it can be heard. I have made no point of argument that one should do so. 

Then why argue? What you are saying here is it has been a pointless exercise to you.

John

I have stated that sampling higher than the nyquist rate on audio signals will produce a better reconstructed signal

I am saying that isn't so. It wont create any better signal. Is that clear enough?

I have made no claim that it can be heard. I have made no point of argument that one should do so. 

Then why argue? What you are saying here is it has been a pointless exercise to you.

Is it clear enough that you are wrong get a frigging oscilloscope. It is the fundamental building block of digital sampling and calculus for that matter. Nyquist quantifies the limits based on a special case. Yes these limits work in the audio domain. Nyquist doesn't say that sampling at higher frequencies won't provide better reconstruction in this case because nyquist doesn't apply to finite time signals..

Is it clear enough that you are wrong get a frigging oscilloscope.

I own two of them.

John

Is it clear enough that you are wrong get a frigging oscilloscope.

I own two of them.

Then run a test. At 44.1k sampling frequency 44100 sample (reading of the amplitude) are taken every second of the incoming finite time analog signal. At 48k sampling frequency 48000 samples (reading of the amplitude) are taken every second of the incoming finite time analog signal. It cannot be disputed that the 48k will provide a better reconstruction of the original analog finite time signal. To what degree and to what worth is what this thread has become about.

It cannot be disputed that the 48k will provide a better reconstruction of the original analog finite time signal. To what degree and to what worth is what this thread has become about.

Wrong. All a 48 kHz sample rate will do is allow a 24 kHz signal to pass. Yes that 24 kHz signal will be accurate. But, and this is the point, at a 44.1 kHz sample rate a 20 kHz signal will also pass and it will be just as accurate as the same signal sampled at 48 kHz. This is what you don't get.

John

It cannot be disputed that the 48k will provide a better reconstruction of the original analog finite time signal. To what degree and to what worth is what this thread has become about.

Wrong. All a 48 kHz sample rate will do is allow a 24 kHz signal to pass. Yes that 24 kHz signal will be accurate. But, and this is the point, at a 44.1 kHz sample rate a 20 kHz signal will also pass and it will be just as accurate as the same signal sampled at 48 kHz. This is what you don't get.

 
Once again you completely miss the point and continue to post incorrect information. I'm just tired of reading nonsense being posted in regards to nyquist and finite time signals. It is unfortunate that no one seems to understand the difference in finite time signals and infinite time signals. You and UnderTow assume that 44.1k will be the standard for all time. It will not be. In fact in less than two decades variable frequency sampling will be the standard. Have a good day.

I have stated that sampling higher than the nyquist rate on audio signals will produce a better reconstructed signal.

Well, there is a degree of truth to this. But it's irrelevant. Bear with me on this, rabeach.

First, "sampling higher than the nyquist rate" is meaningless. There is no such thing as a "nyquist rate". There is, however, a "Nyquist frequency", but it's not any specific frequency. The term is used to describe the minimum sample frequency for a given bandwidth. Raising the sample frequency increases the possible bandwidth that can be captured, so the Nyquist frequency is determined by the highest audio frequency you want to capture.

Second, the sampling theorem specifically applies to a band-limited system. That means you decide up front what bandwidth you need and go from there. There is no such thing as sampling an unlimited bandwidth. You always start with the premise that there is a specific bandwidth you're interested in.

Why is this "band-limited system" idea so important? Because it determines what a properly reconstructed signal should look like. For example, if you sample a 20KHz square wave at 44.1KHz the reconstructed waveform will NOT be square, it will be a sine wave. (This, I think, is where you're going off track, because if you were to increase the sample rate you would indeed get something more closely resembling a square wave - although still far from square).

Why am I willing to accept a 20KHz sine wave as a reasonable facsimile of the original square wave? Because I cannot hear any difference between the two! Not just me, nobody can. Not even dogs and bats.

That's because it's the odd harmonics that make a square wave square, and what make it sound different from other waveshapes. For a 20KHz fundamental, the frequency of the first odd harmonic is 60KHz, the next is 100KHz, and the next is 1400KHz - all of them far beyond audibility.  Losing them does not change the perceived sound at all.

So if you start with the presumption that only audible frequencies need to be recorded, then there is no need to capture anything beyond 20KHz. That is the definition of a band-limited system, the prerequisite for the application of sampling theory, and setting that maximum frequency is what allows us to capture data digitally in the first place.

This idea that frequencies can be just cast away may seem counter-intuitive, but you can easily demonstrate it for yourself. Don't use 20KHz, since most people can't hear that anyway; use 10KHz instead. Using a signal generator, record a 10Khz square wave at the highest sampling rate your interface supports. At 192KHz you can capture the first three harmonics, which won't yield a truly square-looking wave, but it will obviously not be a sine wave, either. Then record a 10Khz sine wave. Now do a blind A/B test to see if you can tell the difference. If your interface is working properly, you won't be able to. The reason is that those extra frequencies you captured simply don't matter because you cannot hear them.

So at the end of the day, you are right: the higher sampling rate will indeed capture a broader bandwidth and thus preserve the original waveform better. However, it doesn't matter in the slightest.