Dave, what makes you say that the conditions are rarely satisfied?
it would imply that the A/D converters are badly implemented but I'm sure someone must be getting things right.
an A/D should employ an anti-aliasing analog filter prior to sampling. how that is implemented is another matter but I'm sure that the analog filter is there.
with scopes it's somewhat a different matter. there never is a filter and you're making assumptions about the nature of the measured signal. assumptions which may be close to or far from truth, having a high sample rate helps you see what's really going on.
though you may be right about not all the conditions being met with Nyquist (hint: steady-state signals).
I seem to recall reading this from you before, and probably I even asked about it before. Any justification for why? And which variety of analog were you thinking of?
Could that be because a digital scope has poor or no reconstruction filters? And possibly poor or no anti-aliasing filters? With inadequate filtering you need a faster sample rate so the unfiltered waveform is a reasonable approximation to the original signal. With proper filtering this faster sampling is not needed.planet10 said:
Your comments about the sampling theorem are often made by various people, but are misguided. Nobody is claiming that digital audio is perfect, but in principle it can get as close to perfection as we are willing to pay for. The constraints are ADC/DAC accuracy, causality issues with the filters (a perfect brick-wall filter would take forever to produce an output) and timing jitter.
while not pretending to get all the math behind this, one thing that has always bugged me with Nyquist is: isn't it implying that the signals composing the input are steady-state (invariant sines)?
I'm thinking this case. it's pretty extreme but nevertheless. say the input signal is a frequency that's pretty close to Nyquist but it's not a steady sine but has an envelope of some type (say a Gaussian window). also say that the window length is small compared to the period of the input sine so that a small number of periods is "caught". do we have enough info to perfectly reconstruct that signal?
I know (think?) that from a mathematical standpoint that kind of signal (amplitude modulated) has content above the carrier but from a nature's point of view that is nothing but a resonance that decays until it's gone.
I'm sure I'm missing something, maybe some DSP guy can shed some light?
When you modulate a signal you create sidebands. Any of these sidebands above the anti-aliasing filter cutoff will be discarded (ideal case) or attenuated/phase shifted (real case). Any remaining sidebands above the Nyquist limit will cause aliasing. Nothing special about this: the sampling theorem requires no components above the Nyquist limit. You can't reproduce signals above the limit, however you produce them. An exponentially decaying sinewave has a wide bandwidth (theoretically infinite), and it will never end, so you can't hear it exactly anyway.
People often seem to think that if a toneburst has a 'fundamental' frequency of 1kHz then the output is more or less 1kHz too. Not quite true, as you have sidebands which may be extensive if the gating is sharp. A sharply gated toneburst might not be exactly reproduced by a digital system, but that is simply because the toneburst has a wide spectrum. Once you remember that you can't hear an infinite spectrum the issue is simply "Did we throw away something which we would have heard?". This is the real issue; everything else is just smoke and confusion.
People often seem to think that if a toneburst has a 'fundamental' frequency of 1kHz then the output is more or less 1kHz too. Not quite true, as you have sidebands which may be extensive if the gating is sharp. A sharply gated toneburst might not be exactly reproduced by a digital system, but that is simply because the toneburst has a wide spectrum. Once you remember that you can't hear an infinite spectrum the issue is simply "Did we throw away something which we would have heard?". This is the real issue; everything else is just smoke and confusion.
exactly!
although I have all the data myself I seem to have some problems integrating everything. I must be turning into some king of subjectivist
I know about the side-bands and I initially wanted to write that the low-pass filter will eliminate them.
I guess that my mistake was to think that the low-pass filtering done by the ear is "special" in some way and the result is different from the anti-alias filtering in the A/D converter. but I guess it's not.
I wasn't necessarily thinking about sharp gating (or compact support as the math guys call it if I recall correctly from the math course) as that would obviously need infinite bandwidth but the more realistic case of a exponentially decaying envelope that models somehow the resonance of a string. but anyway as you said we're not hearing it anyway (the side-bands mean).
I can't believe it took me so long to finally get it, thanks for slapping me back to reality
The ear is more like an overlapping set of bandpass filters, but it is a physical object and so is subject to the same laws of physics and maths as any filter or set of filters. Assuming we can't hear DC, and we can't hear infinite frequencies, means we can't exactly hear almost everything else accurately. People often try to contrast the weaknesses (real or imagined) of digital audio against some perfection - but the perfection does not exist. Our ears have a finite bandwidth, and real mikes and speakers have finite bandwidths. In many cases these are the limiting factors.
yes, I've seen many people talking about the auditory system as if it were the embodiment of mathematical perfection.
speaking of which, it might be my poor interpretation but I remember seeing some references to the fact that we don't perceive sound only in the frequency domain. given what I know and understand about ear structure there is nothing supporting this. or is there?
speaking of which, it might be my poor interpretation but I remember seeing some references to the fact that we don't perceive sound only in the frequency domain. given what I know and understand about ear structure there is nothing supporting this. or is there?
The frequency and time domains are different ways of looking at exactly the same thing. They are completely equivalent, apart from waveform discontinuities and infinities (which never happen in real life). You choose the one which makes the issue under discussion easier to understand/calculate/model, but you could always use the other one with more work and hard thinking. Many things work best using an approximation of a mixed model: a 1kHz toneburst lasting 0.1s is an example of a mixed time/frequency description.
My understanding is that the ear works mainly via its filter banks, which is why the phase of a harmonic/overtone makes little or no difference to the perceived sound even though it makes a huge difference in the waveform. It is conceivable that it also has the ability to perceive sharp transients, but I don't know. It may work by comparing firing times of the filter banks.
My understanding is that the ear works mainly via its filter banks, which is why the phase of a harmonic/overtone makes little or no difference to the perceived sound even though it makes a huge difference in the waveform. It is conceivable that it also has the ability to perceive sharp transients, but I don't know. It may work by comparing firing times of the filter banks.
yes time domain and frequency domain are the same thing, that's settled. but I was thinking of the scenario where very sharp transients which would imply bandwidths beyond 20kHz are allegedly distinguishable from their low-pass filtered versions.
I feel like adding that what we refer to as transients with real music never looks like a step function but rather a sine with a fast rising envelope.
I feel like adding that what we refer to as transients with real music never looks like a step function but rather a sine with a fast rising envelope.
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Hi
Have you seen the paper :-
Eyes as Fenestrations to the Ears. A Novel mechanism for High Frequency
& Ultrasonic Hearing by Martin Lenhardt Tinnitus Institute.
Http://www.tinnitusjournal.com/detalke_artigo.asp?id=109
Basically in this paper the author proposes that the eye/brain
soft tissue is able to transmit ultrasonics in the band 25KHz
to 65Khz to the ear and that the brain seems to respond
to these frequencies in the perception of music.
Not entirely on topic but could have a bearing on comments
on the limits of audiability in humans.
Its all beyond me but I wonder if there is anyone wth more
knowledge on this subject who would care to comment?
Maybe it can explain why I seem to still be able to hear
hf at my advanced age.
Have you seen the paper :-
Eyes as Fenestrations to the Ears. A Novel mechanism for High Frequency
& Ultrasonic Hearing by Martin Lenhardt Tinnitus Institute.
Http://www.tinnitusjournal.com/detalke_artigo.asp?id=109
Basically in this paper the author proposes that the eye/brain
soft tissue is able to transmit ultrasonics in the band 25KHz
to 65Khz to the ear and that the brain seems to respond
to these frequencies in the perception of music.
Not entirely on topic but could have a bearing on comments
on the limits of audiability in humans.
Its all beyond me but I wonder if there is anyone wth more
knowledge on this subject who would care to comment?
Maybe it can explain why I seem to still be able to hear
hf at my advanced age.
Last time I checked GoldWave's sample rate convertor was sheer crap. That is almost a way to ensure that differences will be heard.
If one aims to test the hypothesis that a sample rate above 44.1kHz is required then one should at the very least employ only the best possible SRCs.
SRC Comparisons
--
Oops. My impatience. Just saw that Goldwave already got decently trashed, and vastly better alternatives suggested.
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Werner, thanks for the link. Despite the crappy src, I couldn't hear a difference, and after rechecking his settings, Pano couldn't either. Ears are far more tolerant than measurement instruments, apparently.
edit: the data on that link is from an older version. Mine is 5.66. Don't know if that makes a difference, but certainly the improvement that they show from the older version is significant.
edit: the data on that link is from an older version. Mine is 5.66. Don't know if that makes a difference, but certainly the improvement that they show from the older version is significant.
WOW! Real research on how there is another route for the brain to perceive sound!
That was 30+ years ago, it was an insight based on the detail of what we were discussing in class.
At the time there was no digital
dave
lends new meaning to doing anything "by the seat of your pants", but how to calibrate for varying degrees of "shrinkage"?
in mechanical dynamic measurements 10-20x faster sampling is preferred since phase is important to most uses of the digitized information, steep anti-alias analog filters are poor close to cutoff
if you need to close a motion control loop around the ADC/DAC latency, anti-alias, reconstruction filter added phase shift then you need the “oversampling” much higher than the loop unity gain intercept, dominant mechanical time constants
but apparently our hearing is much less sensitive to (R/L channel matching) phase shift in the highest audio octave so even the original high order analog anti-alias filtering for CD digital audio wasn't judged a audible problem
in practice today almost everything in digital audio is highly oversampled, internally digitally filtered, decimated inside modern ADC chips
the ADC internal digital filtering can be linear phase
and of course mastering practice is to use high sample rate, bit depth until the final step - CD 16/44 is just (arguably) adequate for consumer music distribution where very little additional signal processing is anticipated
if you need to close a motion control loop around the ADC/DAC latency, anti-alias, reconstruction filter added phase shift then you need the “oversampling” much higher than the loop unity gain intercept, dominant mechanical time constants
but apparently our hearing is much less sensitive to (R/L channel matching) phase shift in the highest audio octave so even the original high order analog anti-alias filtering for CD digital audio wasn't judged a audible problem
in practice today almost everything in digital audio is highly oversampled, internally digitally filtered, decimated inside modern ADC chips
the ADC internal digital filtering can be linear phase
and of course mastering practice is to use high sample rate, bit depth until the final step - CD 16/44 is just (arguably) adequate for consumer music distribution where very little additional signal processing is anticipated
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