|
|
Post by Casey Leedom on Apr 12, 2018 10:12:11 GMT -5
No. Nothing has infinite resolution. Not digital, not analogue. Everything has a Frequency Response Function.
Casey
|
|
|
|
Post by pedrocols on Apr 12, 2018 10:17:58 GMT -5
I always wonder what is the benefit in real word listening to a FR above 20/20. How is it better if NOBODY can hear it?
|
|
|
|
Post by 405x5 on Apr 12, 2018 10:42:11 GMT -5
Just turn it down a little don't turn it up to 11...😎 Dynamic range is relevant at LOW listening levels as well. Analog is inferior at both. Bill |
|
DYohn
Emo VIPs 
Posts: 18,493
|
Post by DYohn on Apr 12, 2018 11:51:12 GMT -5
Yes. The full band FR and 96db dynamic range of 16/44.1 PCM exceeds that of analog recording devices. I mean timewise. Is there anything that may not get captured? Or is it "infinite resolution" timewise as long as it's within the FR and DR? Does 24 bit at 44.1 khz give you any advantage time related in capturing vs 16 bit 44.1? 24 bit sampling increases the dynamic range to around 120db, so that is an advantage, other than that... time wise? Not sure I follow. There is no timing issue with digital recording that is significant to audio. What do you mean? |
|
|
|
Post by garbulky on Apr 12, 2018 12:02:43 GMT -5
I mean timewise. Is there anything that may not get captured? Or is it "infinite resolution" timewise as long as it's within the FR and DR? Does 24 bit at 44.1 khz give you any advantage time related in capturing vs 16 bit 44.1? 24 bit sampling increases the dynamic range to around 120db, so that is an advantage, other than that... time wise? Not sure I follow. There is no timing issue with digital recording that is significant to audio. What do you mean? Like if there were multiple instruments playing all just a tiny bit apart from each other in time. At what points in time does the codec capture audio information? Where's the limit or time steps? It can't capture it from infinite points in time because it a 16/44.1 stream caps out at 1400 kbps and not infinite data. |
|
DYohn
Emo VIPs
Posts: 18,493
|
Post by DYohn on Apr 12, 2018 12:21:54 GMT -5
But then when the digital information is decoded back to analog, it returns to being if not "infinite," continuous. The idea that digital is "discrete" so therefor must chop up the sound into samples is not a true reflection of the end result, it is a gross over-simplification based on mentally dissecting the nature of digital data not on an understanding of how an A-D-A process actually works. The sound in and the sound out are both continuous analog signals, they are simply being stored (and perhaps processed) as digital representations. Nothing is missed. But to answer your question directly, at 44.1 kHz the "time base" for each sample would be 1/44100 of a second. So in theory if there was information that happened with a duration of less than that time, it could be "missed."
The likelihood of this in an audio or video signal is not only remote, it is for all practical purposes impossible.
|
|
|
|
Post by garbulky on Apr 12, 2018 12:26:02 GMT -5
But then when the digital information is decoded back to analog, it returns to being if not "infinite," continuous. The idea that digital is "discrete" so therefor must chop up the sound into samples is not a true reflection of the end result, it is a gross over-simplification based on mentally dissecting the nature of digital data not on an understanding of how an A-D-A process actually works. The sound in and the sound out are both continuous analog signals, they are simply being stored (and perhaps processed) as digital representations. Nothing is missed. But to answer your question directly, at 44.1 kHz the "time base" for each sample would be 1/44100 of a second. So in theory if there was information that happened with a duration of less than that time, it could be "missed." The likelihood of this in an audio or video signal is not only remote, it is for all practical purposes impossible. Yes I understand that when PCM is converted it's a continuous analog signal and not a bunch of steps. So 44.1 khz the time base is 1/44100 of a second. You mentioned it would be nearly impossible for any information to be missed. Is that because there's only so many frequencies between 20 and 20khz that could happen between 1/441000 of a second and the next 1/441000? I.e. 1/441000 a second can only have so many frequencies happening between it and the next 1/441000 second in time? I guess what do you mean it's practically impossible? Also....does 24 bit 44.1 khz change this "time resolution" at all vs 16 bit? |
|
|
|
Post by Casey Leedom on Apr 12, 2018 12:38:50 GMT -5
Like if there were multiple instruments playing all just a tiny bit apart from each other in time. At what points in time does the codec capture audio information? Where's the limit or time steps? It can't capture it from infinite points in time because it a 16/44.1 stream caps out at 1400 kbps and not infinite data. So if you're asking to what resolution a Digital Sampling Rate can distinguish between the starting times of various instruments, then that's simply the corresponding Time Period of the Sampling Rate. If you're asking the Maximum Representable Frequency, then that's the Sampling Rate/2 (with the caveats of Aliasing issues that' have already been discussed). If you're asking about what happens with the Signal Amplitude when there are two instruments being transcoded into Digital, then resulting Signal Amplitude will be a "sum" of the Amplitudes of the two separate instruments. (But I don't think it's a simple sum.) For this, the Recording Engineer has to make sure that the "Recording" fits within the Digital Representation of the Sampling. If you're asking what happens when two frequencies are present which are very close to each other, then you end up with a third frequency which is the Beat Frequency between the first two frequencies. If you've ever tuned a Guitar, you'll be familiar with how that Beat Frequency slows down as the two frequencies get closer and closer to each other. There's also something called Intermodulation Distortion, but I'm not sure that a Digital Signal is susceptible to that. KeithL will know more about this. Casey |
|
|
|
Post by Casey Leedom on Apr 12, 2018 12:44:07 GMT -5
Yes I understand that when PCM is converted it's a continuous analog signal and not a bunch of steps. So 44.1 khz the time base is 1/44100 of a second. You mentioned it would be nearly impossible for any information to be missed. Is that because there's only so many frequencies between 20 and 20khz that could happen between 1/441000 of a second and the next 1/441000? I.e. 1/441000 a second can only have so many frequencies happening between it and the next 1/441000 second in time? I guess what do you mean it's practically impossible? Also....does 24 bit 44.1 khz change this "time resolution" at all vs 16 bit? For understanding the maximum frequency representable with a given Sampling Rate, you really need to start diving into the Nyquist–Shannon sampling theorem16- versus 24-bit samples has nothing to do with this. This has to do with the gradations of Amplitude representable, from softest to loudest. And, if there's a Noise Floor in the system, then you can boost the Signal above the Noise Floor in a 24-bit representation and still maintain a very good Signal-to-Noise Ratio. Casey |
|
DYohn
Emo VIPs
Posts: 18,493
|
Post by DYohn on Apr 12, 2018 12:44:22 GMT -5
garbulky, I recommend you research "Nyquist frequency."
|
|
KeithL
Administrator 
Posts: 10,273
|
Post by KeithL on Apr 12, 2018 14:07:09 GMT -5
The bit depth determines the accuracy with which you can record the value of each sample. In general, this relates to dynamic range (or S/N) and not to frequency response or time accuracy. So a 24/44k recording has more dynamic range, or a lower noise floor, than a 16/44k file... but the same frequency response. As far as "other stuff", when it comes to discussing mathematical ideas like "signals", and how they relate to real things, you always end up sort of down the rabbit hole. For example, when we talk about A/D and D/A conversions, part of the requirement is that we limit the bandwidth of the signals involved. So, when we look at the outputs of various DACs, and at the impulse response with various filters, we must also remember that the DAC will NEVER be asked to play such a signal. A single one-sample pulse contains a range of frequencies, some of which exceed the range of frequencies that are supposed to be allowed by the band-limiting filter, which is a mandatory requirement for the process. Therefore, while a useful test signal, in terms of what the DAC will be asked to play, it is an invalid signal. This matters because, if the proper filtering were applied, our nice sharp impulse would be spread out - with both pre-ringing and post-ringing. And, if we used this real-world signal to compare filters, we might well find that the "obvious differences" between our various filter choices weren't visible, or audible, at all. In a similar vein, no DAC can reproduce a good looking square wave, no microphone can record one, and no vinyl disc can deliver a perfect one either. And, yes, Delta-Sigma modulators introduce time errors.... but nowhere near as bad as the ones introduced by record cutting lathes and phono cartridges. The reality is that, if we record something onto a CD, the band-limiting required as part of the process will limit the frequency response... and the bit depth will limit the dynamic range. In addition to that, various error mechanisms in the process of converting the audio to digital, and then back to analog, will introduce further errors and limitations. When CDs were developed, both the bit depth and the sample rate were determined as "just good enough that nobody will hear any of the limitations".... based on the limitations of human hearing - as understood at the time. However, the sampling theorem does specify continuous sine waves, so the time resolution may be somewhat less than we expect with non-continuous signals. But, again, this error was deemed to be "totally inaudible" at the time. And DACs themselves don't operate precisely as the theory predicts (for example, DACs do not use a "real SinC function"; they use "a physical circuit whose output approximates a SinC function over a certain range". But, in the end, all of these error mechanisms come under limitations of the chosen sample rate and bit depth (because we can reduce them by moving to a larger bit depth or a higher sample rate). To put all this in a rather more generalized form..... The parameters chosen for CDs were based on the current ideas about the limits of human hearing - when taken under specific conditions. For example, "it is widely accepted that the majority of humans hear a range between 20 hz and 20 kHz WHEN TESTED WITH CONTINUOUS SINE WAVES". There is now some dispute whether, under certain other conditions, humans may be able to hear a wider range of frequencies. There is also dispute whether we can sense or detect timing errors that infer a sensitivity to time differences that equate to frequencies above 20 kHz. (In other words, when you limit the bandwidth of a signal to 20 kHz, you may not hear anything missing, but you may still notice a difference - like a slight shift in sound stage.) Note, however, that most recording microphones, and pretty well all analog master tapes, have much the same limitations as CDs. Humans also seem able to distinguish the difference between various types and amounts of filter ringing.... even amounts below what are assumed by some people to be "the limits of audibility". The short answer is that it is POSSIBLE that the limitations placed on CDs do in fact produce subtle differences with certain content. I'm not convinced either way - so I would consider it to be "still in question"; but, given that situation, and the low cost of storage space, I'd rather be safe and use the higher sample rate when available. And the obvious solution is to use 24/96k..... which has much wider limits (and whose limits exceed the capabilities of both vinyl and human hearing by a nice solid safety margin). However, to answer the question... ignoring the question of audibility... using 24 bits instead of 16 bits would not improve timing accuracy... In some ways the time resolution is infinite; in others it is somewhat limited by factors related to the sample rate. If you want to improve timing accuracy, or the accuracy with which small time differences are resolved and stored, you want to change the sample rate... from 44k to 96k. Yes. The full band FR and 96db dynamic range of 16/44.1 PCM exceeds that of analog recording devices. I mean timewise. Is there anything that may not get captured? Or is it "infinite resolution" timewise as long as it's within the FR and DR? Does 24 bit at 44.1 khz give you any advantage time related in capturing vs 16 bit 44.1? |
|
|
|
Post by Casey Leedom on Apr 12, 2018 14:26:46 GMT -5
...When CDs were developed, both the bit depth and the sample rate were determined as "just good enough that nobody will hear any of the limitations".... based on the limitations of human hearing - as understood at the time.... This is probably my biggest gripe about Red Book. Because 44.1kHz was "just good enough to probably not be audible", that's let a whole bunch of Whack Job Audiophiles and Charlatans promote all sorts of crazy things from Green Pens to CD Weights. I really wish that Red Book had been 96kHz/24bits from the get go. Casey |
|
KeithL
Administrator
Posts: 10,273
|
Post by KeithL on Apr 12, 2018 15:34:13 GMT -5
Actually your explanation is correct... but you missed one important part. Any valid 44k digital audio signal MUST BY DEFINITION be band-limited to 22 kHz. Any event whose period was less than a single sample at 44k would be far above that limit, and so would be excluded by the band-limiting filter. (And the highest frequency that the band-limiting filters will allow will have a period of more than two samples in duration.) If we were talking about an analog source, that high frequency event would be cut out by the band-limiting filters in the ADC - because it's above 22 kHz. If you tried to "make" it in a digital editor, most of the good ones will prevent you, or will alter it to agree with "what is allowed to be there". For example, if you try to draw a square wave, most editors will give you a nice square wave, with the ringing that would have been created by the band-limit filter already "pre-installed" for you. (They "know" about the band-limits of the sample rate you've chosen and force whatever you do into compliance with them.) Another example would be to generate several seconds of a pure tone in something like Audition. Now cut it so all that's left is 1/2 second of that pure tone... and look at the spectrum view. You'll see your tone... with the little bobble at each end from the ringing when you cut it... and the spectrum view will show a spike of high frequencies at each end that represent the spectrum of the discontinuity from the cut. You could certainly create a digital audio file that contained invalid data - just manually edit a 44k digital audio file so that one sample is a positive value and all other samples are zero.) However, since the file itself is invalid, even if your player program is willing to pass it on, you can't complain that whatever the DAC gives you when you play it is "incorrect".  But then when the digital information is decoded back to analog, it returns to being if not "infinite," continuous. The idea that digital is "discrete" so therefor must chop up the sound into samples is not a true reflection of the end result, it is a gross over-simplification based on mentally dissecting the nature of digital data not on an understanding of how an A-D-A process actually works. The sound in and the sound out are both continuous analog signals, they are simply being stored (and perhaps processed) as digital representations. Nothing is missed. But to answer your question directly, at 44.1 kHz the "time base" for each sample would be 1/44100 of a second. So in theory if there was information that happened with a duration of less than that time, it could be "missed." The likelihood of this in an audio or video signal is not only remote, it is for all practical purposes impossible. |
|
KeithL
Administrator
Posts: 10,273
|
Post by KeithL on Apr 12, 2018 15:35:46 GMT -5
I agree.... but there's a reason why it's not. The physical capacity of the discs they were able to conveniently make at the time was a limiting factor. They would have had to drop the time down to 30 minutes to go up to 96k.... and they decided more time was more important. ...When CDs were developed, both the bit depth and the sample rate were determined as "just good enough that nobody will hear any of the limitations".... based on the limitations of human hearing - as understood at the time.... This is probably my biggest gripe about Red Book. Because 44.1kHz was "just good enough to probably not be audible", that's let a whole bunch of Whack Job Audiophiles and Charlatans promote all sorts of crazy things from Green Pens to CD Weights. I really wish that Red Book had been 96kHz/24bits from the get go. Casey |
|
|
|
Post by Casey Leedom on Apr 12, 2018 16:16:04 GMT -5
Ah well, if "Physical Media is Dead", then Digital Downloads (and even Streaming) can solve the problem ... :-)
Casey
|
|
KeithL
Administrator
Posts: 10,273
|
Post by KeithL on Apr 12, 2018 16:17:48 GMT -5
You're still "overthinking it". There's air.... and there's air pressure..... which goes up and down.... and that's sound. Things like "frequency" are just ways in which we humans choose to look at how the air pressure goes up and down. There are no such things as "separate frequencies". We store a single number... in the form of a list of numbers, each of which represents that single number at a different point in time. When we talk about a frequency limit what we're really talking about is a limit on how fast the air pressure can change before we become unable to accurately reproduce that movement. So, when we say that "A CD can store frequencies up to 20 kHz" what that means is that, on a CD, we can store numbers that describe the air pressure changing as fast as it would with a 20 kHz sine wave. (And, if it changes faster than that, then our current numbers are inadequate to describe the change properly... which is why we'd better be sure we don't ever ask them to.) The thing that's difficult to get your head around is that, even though we may "take a sample" every 1/44,000 of a second, that doesn't mean that everything that happens between those two samples is ignored. The information about everything that happens between each pair of samples is sort of built INTO the values OF those two samples. (It's really crude, but think of those numbers like beads strung on a cable.... there are limits on how far apart they can be, and how quickly the entire cable can loop up and down to accommodate individual beads.) For example, let's say the voltage at one sample is 1V, and the voltage at the next sample is 2V. Then we KNOW that the voltage HAD TO BE 1.5V at some point between them. Even more than that we KNOW it can't have gone up to 5V for a split second somewhere in the middle. We know this because, in order to do that, it would have had to move very fast, and that fast movement would have had to contain "high frequency information". Except, since we know that we've applied a band-limiting filter, we KNOW that the signal DIDN'T contain that high frequency information.... because the filter wouldn't let it. Therefore, we know that the number had to move gradually from 1V to 2V. The reason a CD will NEVER contain information at 29 kHz is because it isn't ALLOWED to..... (You don't have to check the back seat of your Volkswagen for an elephant because it wouldn't fit... and nobody would let it in... so, if you see two eyes staring from the back seat, you KNOW they don't belong to an elephant.) Likewise, part of the "information" we have stored on that CD is actually contained in the knowledge we have about what CANNOT POSSIBLY be there. We look at the numbers, and sometimes determine that a certain pair of numbers could describe two very different waveforms. However, we know which one is the right one because the other one ISN'T ALLOWED. Part of the way the process is able to work correctly is precisely BECAUSE there are strict limitations on what's allowed. (And, when you hear about things like "distortion due to aliasing" what we're talking about is things that are there because someone bent the rules and wasn't careful enough about excluding what shouldn't be there.) I'm afraid that is a REALLY poetic attempt to describe this without math.... but it's actually pretty close to the truth. But then when the digital information is decoded back to analog, it returns to being if not "infinite," continuous. The idea that digital is "discrete" so therefor must chop up the sound into samples is not a true reflection of the end result, it is a gross over-simplification based on mentally dissecting the nature of digital data not on an understanding of how an A-D-A process actually works. The sound in and the sound out are both continuous analog signals, they are simply being stored (and perhaps processed) as digital representations. Nothing is missed. But to answer your question directly, at 44.1 kHz the "time base" for each sample would be 1/44100 of a second. So in theory if there was information that happened with a duration of less than that time, it could be "missed." The likelihood of this in an audio or video signal is not only remote, it is for all practical purposes impossible. Yes I understand that when PCM is converted it's a continuous analog signal and not a bunch of steps. So 44.1 khz the time base is 1/44100 of a second. You mentioned it would be nearly impossible for any information to be missed. Is that because there's only so many frequencies between 20 and 20khz that could happen between 1/441000 of a second and the next 1/441000? I.e. 1/441000 a second can only have so many frequencies happening between it and the next 1/441000 second in time? I guess what do you mean it's practically impossible? Also....does 24 bit 44.1 khz change this "time resolution" at all vs 16 bit? |
|
|
|
Post by garbulky on Apr 12, 2018 16:42:16 GMT -5
You're still "overthinking it". There's air.... and there's air pressure..... which goes up and down.... and that's sound. Things like "frequency" are just ways in which we humans choose to look at how the air pressure goes up and down. There are no such things as "separate frequencies". We store a single number... in the form of a list of numbers, each of which represents that single number at a different point in time. When we talk about a frequency limit what we're really talking about is a limit on how fast the air pressure can change before we become unable to accurately reproduce that movement. So, when we say that "A CD can store frequencies up to 20 kHz" what that means is that, on a CD, we can store numbers that describe the air pressure changing as fast as it would with a 20 kHz sine wave. (And, if it changes faster than that, then our current numbers are inadequate to describe the change properly... which is why we'd better be sure we don't ever ask them to.) The thing that's difficult to get your head around is that, even though we may "take a sample" every 1/44,000 of a second, that doesn't mean that everything that happens between those two samples is ignored. The information about everything that happens between each pair of samples is sort of built INTO the values OF those two samples. (It's really crude, but think of those numbers like beads strung on a cable.... there are limits on how far apart they can be, and how quickly the entire cable can loop up and down to accommodate individual beads.) For example, let's say the voltage at one sample is 1V, and the voltage at the next sample is 2V. Then we KNOW that the voltage HAD TO BE 1.5V at some point between them. Even more than that we KNOW it can't have gone up to 5V for a split second somewhere in the middle. We know this because, in order to do that, it would have had to move very fast, and that fast movement would have had to contain "high frequency information". Except, since we know that we've applied a band-limiting filter, we KNOW that the signal DIDN'T contain that high frequency information.... because the filter wouldn't let it. Therefore, we know that the number had to move gradually from 1V to 2V. The reason a CD will NEVER contain information at 29 kHz is because it isn't ALLOWED to..... (You don't have to check the back seat of your Volkswagen for an elephant because it wouldn't fit... and nobody would let it in... so, if you see two eyes staring from the back seat, you KNOW they don't belong to an elephant.) Likewise, part of the "information" we have stored on that CD is actually contained in the knowledge we have about what CANNOT POSSIBLY be there. We look at the numbers, and sometimes determine that a certain pair of numbers could describe two very different waveforms. However, we know which one is the right one because the other one ISN'T ALLOWED. Part of the way the process is able to work correctly is precisely BECAUSE there are strict limitations on what's allowed. (And, when you hear about things like "distortion due to aliasing" what we're talking about is things that are there because someone bent the rules and wasn't careful enough about excluding what shouldn't be there.) I'm afraid that is a REALLY poetic attempt to describe this without math.... but it's actually pretty close to the truth. Yes I understand that when PCM is converted it's a continuous analog signal and not a bunch of steps. So 44.1 khz the time base is 1/44100 of a second. You mentioned it would be nearly impossible for any information to be missed. Is that because there's only so many frequencies between 20 and 20khz that could happen between 1/441000 of a second and the next 1/441000? I.e. 1/441000 a second can only have so many frequencies happening between it and the next 1/441000 second in time? I guess what do you mean it's practically impossible? Also....does 24 bit 44.1 khz change this "time resolution" at all vs 16 bit? So what you're saying is it's not time limited because of the amount of time it takes for the fastest wave - say at 20khz to rise and fall. So the time 1/44000th of a second is shorter than the time for the fastest 20 khz wave so a 20 khz wave could NOT have happened between it. |
|
|
|
Post by Casey Leedom on Apr 12, 2018 17:05:28 GMT -5
garbulky, you're walking dangerous ground. Much further and you'll need to take a course on Signal Processing. Now, the Down Side is that it's a freaking hard subject area with lots of complex and non-intuitive mathematics. The Up Side is that you'll be ready for a new and Very Highly Paid Career since SI Experts are hard to come by. Casey
|
|
KeithL
Administrator
Posts: 10,273
|
Post by KeithL on Apr 12, 2018 17:20:30 GMT -5
Errr..... sort of. Let's try it this way. Any event that would have been short enough to happen between two 44k samples would HAVE TO BE OCCURRING at a frequency well above 22 kHz. And, since the mandatory band-limiting filter required for a 44k sample rate BLOCKS everything above 22 kHz, it would not be ALLOWED to be recorded on a CD. (Of course, the assumption is that, since we can't hear above 22 kHz, there would be no reason to include it... because we couldn't hear it anyway.) Now, if what you were talking about was a phase difference between two signals, each of which was well below 22 kHz, but where the difference between them was really small, then that would still be recorded correctly. Since each of the two signals is actually recorded in a whole bunch of samples, there's plenty of detail in that information to determine exactly where each one is. Unfortunately, a lot of this stuff is not at all intuitive.... Which means you have to either be brilliant enough to read the math itself like writing.... Or you have to believe the explanations we're given. (And, unfortunately, there are a lot of bogus explanations and bits of incorrect information out there.) You're still "overthinking it". There's air.... and there's air pressure..... which goes up and down.... and that's sound. Things like "frequency" are just ways in which we humans choose to look at how the air pressure goes up and down. There are no such things as "separate frequencies". We store a single number... in the form of a list of numbers, each of which represents that single number at a different point in time. When we talk about a frequency limit what we're really talking about is a limit on how fast the air pressure can change before we become unable to accurately reproduce that movement. So, when we say that "A CD can store frequencies up to 20 kHz" what that means is that, on a CD, we can store numbers that describe the air pressure changing as fast as it would with a 20 kHz sine wave. (And, if it changes faster than that, then our current numbers are inadequate to describe the change properly... which is why we'd better be sure we don't ever ask them to.) The thing that's difficult to get your head around is that, even though we may "take a sample" every 1/44,000 of a second, that doesn't mean that everything that happens between those two samples is ignored. The information about everything that happens between each pair of samples is sort of built INTO the values OF those two samples. (It's really crude, but think of those numbers like beads strung on a cable.... there are limits on how far apart they can be, and how quickly the entire cable can loop up and down to accommodate individual beads.) For example, let's say the voltage at one sample is 1V, and the voltage at the next sample is 2V. Then we KNOW that the voltage HAD TO BE 1.5V at some point between them. Even more than that we KNOW it can't have gone up to 5V for a split second somewhere in the middle. We know this because, in order to do that, it would have had to move very fast, and that fast movement would have had to contain "high frequency information". Except, since we know that we've applied a band-limiting filter, we KNOW that the signal DIDN'T contain that high frequency information.... because the filter wouldn't let it. Therefore, we know that the number had to move gradually from 1V to 2V. The reason a CD will NEVER contain information at 29 kHz is because it isn't ALLOWED to..... (You don't have to check the back seat of your Volkswagen for an elephant because it wouldn't fit... and nobody would let it in... so, if you see two eyes staring from the back seat, you KNOW they don't belong to an elephant.) Likewise, part of the "information" we have stored on that CD is actually contained in the knowledge we have about what CANNOT POSSIBLY be there. We look at the numbers, and sometimes determine that a certain pair of numbers could describe two very different waveforms. However, we know which one is the right one because the other one ISN'T ALLOWED. Part of the way the process is able to work correctly is precisely BECAUSE there are strict limitations on what's allowed. (And, when you hear about things like "distortion due to aliasing" what we're talking about is things that are there because someone bent the rules and wasn't careful enough about excluding what shouldn't be there.) I'm afraid that is a REALLY poetic attempt to describe this without math.... but it's actually pretty close to the truth. So what you're saying is it's not time limited because of the amount of time it takes for the fastest wave - say at 20khz to rise and fall. So the time 1/44000th of a second is shorter than the time for the fastest 20 khz wave so a 20 khz wave could NOT have happened between it. |
|
|
|
Post by audiosyndrome on Apr 12, 2018 18:54:21 GMT -5
Like I said earlier in response to post one, for all practical purposes YES.
Russ
|
|
