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Vinyl is equivalent to which digital bit-depth and sampling rate?
pdq
post Mar 24 2012, 14:05
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If such jitter were a problem (which it is not) then it is conceivable that a reference tone could be added into the analog signal, then filtered out of the digital data. Of course, the analog reference tone is likely to have much more jitter than the A/D.
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Ethan Winer
post Mar 24 2012, 20:05
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QUOTE (icstm @ Mar 22 2012, 07:45) *
all those ppl who were happy with Vinyl are now seeking better than CD sound quality through their SACDs and the general discussion on >16/44 formats!

Yes, and I see this in pro audio circles too. The same recording engineers who love analog tape lament that even the best digital converters aren't transparent enough for them. Sheesh.

--Ethan


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DonP
post Mar 25 2012, 12:41
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QUOTE (pdq @ Mar 24 2012, 09:05) *
If such jitter were a problem (which it is not) then it is conceivable that a reference tone could be added into the analog signal, then filtered out of the digital data. Of course, the analog reference tone is likely to have much more jitter than the A/D.


No reason to think A/D jitter is any less of a problem than D/A jitter. Just like non-OFC power lines going down the highway are just as much a problem as a non-gourmet power line from the wall to your amplifier.
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Woodinville
post Mar 26 2012, 10:03
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QUOTE (Ethan Winer @ Mar 24 2012, 12:05) *
QUOTE (icstm @ Mar 22 2012, 07:45) *
all those ppl who were happy with Vinyl are now seeking better than CD sound quality through their SACDs and the general discussion on >16/44 formats!

Yes, and I see this in pro audio circles too. The same recording engineers who love analog tape lament that even the best digital converters aren't transparent enough for them. Sheesh.

--Ethan


It's amazing what you can do with a bit of oversampling and M/S distortion.


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Fandango
post Mar 26 2012, 10:18
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QUOTE (icstm @ Mar 22 2012, 13:45) *
^^^ so isn't quite funny that all those ppl who were happy with Vinyl are now seeking better than CD sound quality through their SACDs and the general discussion on >16/44 formats!

Yep, they live and breathe the excluded middle. laugh.gif
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Arnold B. Kruege...
post Apr 15 2012, 12:42
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QUOTE (Fandango @ Mar 26 2012, 05:18) *
QUOTE (icstm @ Mar 22 2012, 13:45) *
^^^ so isn't quite funny that all those ppl who were happy with Vinyl are now seeking better than CD sound quality through their SACDs and the general discussion on >16/44 formats!

Yep, they live and breathe the excluded middle. laugh.gif


It's all about bragging rights.
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icstm
post Apr 16 2012, 09:49
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QUOTE (Woodinville @ Mar 26 2012, 09:03) *
QUOTE (Ethan Winer @ Mar 24 2012, 12:05) *
QUOTE (icstm @ Mar 22 2012, 07:45) *
all those ppl who were happy with Vinyl are now seeking better than CD sound quality through their SACDs and the general discussion on >16/44 formats!

Yes, and I see this in pro audio circles too. The same recording engineers who love analog tape lament that even the best digital converters aren't transparent enough for them. Sheesh.

--Ethan


It's amazing what you can do with a bit of oversampling and M/S distortion.
I am clearly having a Monday morning sydrome...
Why are they using those things? unsure.gif
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cdroid
post Sep 2 2014, 07:36
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So I didn't read each and every one of these posts, but I wanted to weigh in on something that I thought would help your understanding. Most of what I am about to say is a summary of information I got from a conversation with one of my audio engineering instructors. The rest is information from various course books I have had to read as well as some of my own conclusions from all this material.

Your original question was what the sample rate and bit depth equivalents are for vinyl, and someone already accurately answered that it is 44k and 12 bit. Your next question was whether or not someone would just as much enjoy a digital recording at the same specs and the answer is too complicated to have a yes or no answer, but theoretically yes. Here is some elaboration on the subject. For starters, I will point out two factors that commonly cause vinyl to have a "better" sound than digital formats.
1. The most common way we listen to music now is by MP3 or some other "lossy" file type. What I mean by "lossy" is that an MP3 (and some other common file types) are actually compressed; the file has pieces of information that are removed and then approximately replaced during playback. The problem with this is that the lost information is never truly recovered with great accuracy after it has been compressed. We also need a DAC (digital to analog converter) to play back digital files. The DAC takes the ones and zeros stored on the computer and translates them to sound. Most people are simply using the DAC that is built into their portable MP3 player or computer, which typically doesn't sound very good.
2. Vinyl playback systems have a magnetic system that actually smooths over the choppiness of what can be considered gaps between the bit positions and samples. High quality DACs would have similar responses but as I have already discussed, most people do not use high quality DACs.

So what I hope I just properly explained is that although digital has by far surpassed analog, vinyl typically sounds better because the digital delivery systems we use have not caught up to the quality that is available.
Let me suggest that any good audio system will have good preamps, good amps, and good speakers. A good vinyl system will also have high quality cartridges and a good digital system will have high quality, lossless audio files and good DACs. Failing to have high quality components in either playback system will cause it to sound inferior when compared to the other.
Also consider that although digital recording and storage has surpassed analog, the digital signal processing has not yet surpassed the quality of analog signal processing. Consider that a song completely recorded and mixed in the box (on a computer with no analog gear besides the ADC and DAC) will sound inferior to the same song mixed on comparable analog gear. Professional studios will typically have all their microphones run through an analog soundboard with the direct outs of each channel running to a Pro Tools HD rig where it is recorded. Then to mix the Pro Tools HD rig is sent back to the channel where the audio engineer will mix (sometimes aided by plugins in Pro Tools) on the analog board with analog gear inserted on the channels as need. A stereo mix-down will be recorded back to the Pro Tools HD rig instead of to tape. A digital recording will likely not sound better than an analog recording if the quality analog gear is absent. However, plugins are catching up as more processing power becomes available and many plugins have become indistinguishable from their analog counterparts to the untrained ear.

Now I hope I can explain why digital actually is better than vinyl. For starters, Vinyl can be scratched and warped while these and other imperfections are not found in digital. Also, it only takes 44k and 12 bit to surpass analog, but modern Pro Tools HD rigs can actually go up to 192k and 32bit. With a high quality playback system, a lossless audio file with these specs will blow any analog system out of the water. Also, vinyl tends to have a serious drop-off in frequency response after about 17k. You'll notice older people typically prefer vinyl, but that's because you tend to lose hearing over 16k as you age. I would also speculate that they've been listening to vinyl for long enough that the imperfections (like the pops and clicks and crackling of vinyl that I don't really enjoy) have actually become part of the musical experience to them. Digital audio obviously doesn't have this 17k drop-off, so to younger ears there is actually more information on digital audio that can be defined in layman's terms as 'air' or 'presence'. This would greatly increase the tone of a digital recording since many of those tones above 17k are part of the harmonic overtone series on an instrument (I won't even try to explain that one, google it if you don't know it) which would make a recording sound closer to the live performance.

Now there is one more thing to consider about the experience of listening to a vinyl, and I've already touched on the idea that perhaps imperfections have been ingrained as part of the music. It is true that harmonic distortions found in analog gear are sonically pleasing, but we can still experience those tones either in the signal processing stage of mixing or after playback by using tube amps or preamps and other processors after the DAC.
What we need to consider is that music is inherently a spiritual, for lack of a better word, experience. We describe music as being part of your soul, part of that illogical part of you that can't be monitored as brain activity. Music has a quality that is sacred. By listening to music on low quality systems and by putting it everywhere (in the car, in the grocery store, on our commercials, literally everywhere; even in places that drag the music through the mud) we've taken away this sacred quality of music.
On top of that, we turntables are typically plugged into high quality sound systems. Digital audio is usually compressed and played back through your iPod on apple headphones. We've devalued our music this way. If you put on a vinyl, you have to work a little bit to hear the music. First you have to find the vinyl you want and you can't just load up your favorite playlist. Then you have to listen to that album; otherwise you must drop the needle on the song you want and risk damaging your album. You also must typically clean the vinyl with a proper cleaning device and then your vinyl is played back on a high quality system. Going through this whole process physically and mentally prepares you to enjoy the music.
If you really want to enjoy digital music, you must similarly prepare yourself physically and mentally to appreciate the music on a high quality system.

I hope I have done a good job in clarifying all the discussion around vinyl and digital and explained what other people might not have been able to.
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Kohlrabi
post Sep 2 2014, 08:59
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QUOTE (cdroid @ Sep 2 2014, 08:36) *
1. The most common way we listen to music now is by MP3 or some other "lossy" file type. What I mean by "lossy" is that an MP3 (and some other common file types) are actually compressed; the file has pieces of information that are removed and then approximately replaced during playback. The problem with this is that the lost information is never truly recovered with great accuracy after it has been compressed. We also need a DAC (digital to analog converter) to play back digital files. The DAC takes the ones and zeros stored on the computer and translates them to sound. Most people are simply using the DAC that is built into their portable MP3 player or computer, which typically doesn't sound very good.
Everything mixed up with everything else. First, lossy compression is not a huge problem, and properly mastered music from CD, converted to MP3s, will blow any Vinyl record out of the water. And I don't know how you get the impression that most DACs are bad. There might be some bad ones around, but it's even more difficult and challenging setting up a good enough Vinyl playback system. So I can just as well argue that "most people" who listen to Vinyl are getting a subpar experience as well. We cannot know what people use, but there are enough good DACs around.

QUOTE (cdroid @ Sep 2 2014, 08:36) *
2. Vinyl playback systems have a magnetic system that actually smooths over the choppiness of what can be considered gaps between the bit positions and samples. High quality DACs would have similar responses but as I have already discussed, most people do not use high quality DACs.
The quality of even shitty current PC onboard audio DACs far surpasses the theoretical possibilities of Vinyl. And a tiny Sansa Clip+ will beat every Vinyl setup imaginable.

QUOTE (cdroid @ Sep 2 2014, 08:36) *
So what I hope I just properly explained is that although digital has by far surpassed analog, vinyl typically sounds better because the digital delivery systems we use have not caught up to the quality that is available.
No, digital music reproduction has surpassed Vinyl ages ago. The problem is the production/mastering quality of digital recordings.

QUOTE (cdroid @ Sep 2 2014, 08:36) *
Also consider that although digital recording and storage has surpassed analog, the digital signal processing has not yet surpassed the quality of analog signal processing.
Sadly, I don't have any experience in that, but I very much doubt that.

QUOTE (cdroid @ Sep 2 2014, 08:36) *
Now I hope I can explain why digital actually is better than vinyl. For starters, Vinyl can be scratched and warped while these and other imperfections are not found in digital. Also, it only takes 44k and 12 bit to surpass analog, but modern Pro Tools HD rigs can actually go up to 192k and 32bit. With a high quality playback system, a lossless audio file with these specs will blow any analog system out of the water.
Those extra bits are great for processing and production, but will add nothing to the perceptible audio quality. "Redbook" 16 bit and 44.1kHz is good enough for our species.

QUOTE (cdroid @ Sep 2 2014, 08:36) *
By listening to music on low quality systems and by putting it everywhere (in the car, in the grocery store, on our commercials, literally everywhere; even in places that drag the music through the mud) we've taken away this sacred quality of music.
The current problem with modern music is not whether digital is "good enough", or whether "the people" have "good enough" gear, but the production quality of music. Dont' blame the recipient, the customer, for the bad quality of music. The responsible parties are producers, audio engineers, and artists. The customer can just buy what's out there, but the average production quality (in certain genres) has steadily fallen since the early 90s.

QUOTE (cdroid @ Sep 2 2014, 08:36) *
On top of that, we turntables are typically plugged into high quality sound systems. Digital audio is usually compressed and played back through your iPod on apple headphones. We've devalued our music this way. If you put on a vinyl, you have to work a little bit to hear the music. First you have to find the vinyl you want and you can't just load up your favorite playlist. Then you have to listen to that album; otherwise you must drop the needle on the song you want and risk damaging your album. You also must typically clean the vinyl with a proper cleaning device and then your vinyl is played back on a high quality system. Going through this whole process physically and mentally prepares you to enjoy the music.
If you really want to enjoy digital music, you must similarly prepare yourself physically and mentally to appreciate the music on a high quality system.
My opinion is that the whole mystifying of the playback experience is audiophile nonsense talk. You aren't appreciating the music more by using an inferior and inconvenient playback system, you're just cultivating an elitist aura. Everybody can do as he or she pleases, by all means, but the implied sense of superiority by some Vinyl enthusiasts is ridiculous. Be wary, from my experience, if something is termed "audiophile", it sure is special, inconvenient, and sounds bad.

This post has been edited by Kohlrabi: Sep 2 2014, 09:05


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mjb2006
post Sep 2 2014, 09:15
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cdroid, welcome to the forum. You will find that we are not perfect, but we generally don't allow people to get away with repeating folklore as fact, and your post is full of "audiophile" red flags. Some things you do get right, but others, not so much.

QUOTE (cdroid @ Sep 2 2014, 00:36) *
Most people are simply using the DAC that is built into their portable MP3 player or computer, which typically doesn't sound very good.

It "doesn't sound very good"? Really? In what way? DAC technology has been pretty stable for 20, 25 years. Has there been a sudden decline in the quality of DACs lately?

QUOTE (cdroid @ Sep 2 2014, 00:36) *
Vinyl playback systems have a magnetic system that actually smooths over the choppiness of what can be considered gaps between the bit positions and samples. High quality DACs would have similar responses

Well, every phonographic stylus, magnetic or not, traces the groove continuously, producing an analog waveform (or pair of waveforms, for stereo). However, the notion that there's something to "smooth" is a myth. If the waveform is sampled at a particular rate (44100 Hz, for example), then the motion that the stylus is subjected to between the sample points only contributes to frequency content above one-half the sample rate (e.g., frequencies above 22050 Hz, well above the limits of human hearing).

It's kind of a mess, but you should look over Vinyl Myths page in the wiki before making any more dubious claims vinyl.

Also, even if you know some of this stuff already, please take the time to review these presentations by someone way smarter than you and me put together:


QUOTE
Consider that a song completely recorded and mixed in the box (on a computer with no analog gear besides the ADC and DAC) will sound inferior to the same song mixed on comparable analog gear.

You have not defined inferior, so your statement is meaningless. There will be differences, sure, and you may have a preference for one over the other, but how is your preferred sound superior and the other inferior? (rhetorical question, really)

QUOTE
modern Pro Tools HD rigs can actually go up to 192k and 32bit


True, and 32-bit is actually floating-point so it has exponentially greater resolution than 16 or 24-bit integer, but what's the point if it all sounds the same? Do we need ultraviolet, infrared, X-rays and gamma rays in our photo albums, too?

Might as well add to your reading list:


QUOTE
Vinyl tends to have a serious drop-off in frequency response after about 17k.

So does human hearing. As for the frequency limits of vinyl, my understanding is that it really depends on how and when it was mastered, with what cutting equipment. Some cutters roll off within the upper range of human hearing like you say, but others extend a bit further into the ultrasonic territory.

This post has been edited by mjb2006: Sep 2 2014, 09:17
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2Bdecided
post Sep 2 2014, 10:23
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QUOTE (mjb2006 @ Sep 2 2014, 09:15) *
QUOTE (cdroid @ Sep 2 2014, 00:36) *
Consider that a song completely recorded and mixed in the box (on a computer with no analog gear besides the ADC and DAC) will sound inferior to the same song mixed on comparable analog gear.

You have not defined inferior, so your statement is meaningless. There will be differences, sure, and you may have a preference for one over the other, but how is your preferred sound superior and the other inferior? (rhetorical question, really)
He's quoting a widely believed and spectacularly stupid opinion in the pro audio/mixing world: that somehow adding numbers (digital / In The Box) is genuinely inferior and lower quality than adding voltages (analogue / Out Of The Box). Even when the source is digital. Even when the "analogue" mixing requires D>A, mixing, A>D. There's a whole industry set up around providing analogue mixing devices for all-digital rigs.

Where the difference really sits is in the processing applied to the tracks and mix: essentially the comparison is between software plug-ins (in the box) and physical pieces of hardware (out of the box). Obviously these often sound different. It's hard to imagine the level of experimental controls you'd need to apply to ensure that they sounded the same (all other things being equal). Often people get a better result from a stand-alone piece of kit than from a DSP plug-in that some marketing department said was equivalent. This should surprise no one. Sometimes the kit is simply better (not in terms of 24-bit vs 32-bit minutia, but in terms of doing the broad job better), sometimes the fact it's separate means it has buttons and dials which enable the human operator to do a better job, even if the actual processing (if you set the same parameters in the software DSP "equivalent" was the same).

The bizarre thing is that there are many people who call themselves audio engineers who attribute the difference in sound, not to all the above, but to adding voltages rather than numbers.

It's a strange world. And, like the audiophool world, where there's money to be made from their lack of understanding, equipment manufacturers are more than happy to indulge it. A business that only sells to people with a perfect graphs of science and blind testing, who also happen to have excellent hearing and discernment, plus the funds to make expensive purchases - that business is not going to be nearly as profitable as the one that takes money from anyone willing to spend it.

Cheers,
David.
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Arnold B. Kruege...
post Sep 2 2014, 16:10
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QUOTE (cdroid @ Sep 2 2014, 02:36) *
So I didn't read each and every one of these posts, but I wanted to weigh in on something that I thought would help your understanding. Most of what I am about to say is a summary of information I got from a conversation with one of my audio engineering instructors. The rest is information from various course books I have had to read as well as some of my own conclusions from all this material.


The following post might be entitled "Misapprehension city". ;-)

QUOTE
Your original question was what the sample rate and bit depth equivalents are for vinyl, and someone already accurately answered that it is 44k and 12 bit.


Oh, someone was being optimistic about vinyl?

QUOTE
Your next question was whether or not someone would just as much enjoy a digital recording at the same specs and the answer is too complicated to have a yes or no answer, but theoretically yes. Here is some elaboration on the subject. For starters, I will point out two factors that commonly cause vinyl to have a "better" sound than digital formats.


Cut to the chase. If the vinyl version of a song is well mastered, and the digital version is badly mastered then the vinyl version may be able to overcome of of the inherent sonic detriments that are part and parcel of vinyl and actually sound better. That is about it. There is a reason why vinyl was dumped by just about everybody with a brain in the 1980s and it has to do with bad sound quality.


QUOTE
1. The most common way we listen to music now is by MP3 or some other "lossy" file type. What I mean by "lossy" is that an MP3 (and some other common file types) are actually compressed; the file has pieces of information that are removed and then approximately replaced during playback. The problem with this is that the lost information is never truly recovered with great accuracy after it has been compressed. We also need a DAC (digital to analog converter) to play back digital files. The DAC takes the ones and zeros stored on the computer and translates them to sound. Most people are simply using the DAC that is built into their portable MP3 player or computer, which typically doesn't sound very good.


That would be two common misapprehensions in one.

(1) Common lossy file formats are now highly perfected and if you give them a reasonable number of bits to play with and a good encoder the sound quality absolutely and positively blows vinyl into the next universe.

(2) Common DACs are now also highly perfected and now we have to jump over several alternative universes to find one where DAC sound quality, even DACs in $40 digital players, are any kind of an audible problem.


I know the two most common technique to formulate the above misapprehensions which are to do sighted evaluations and to listen to people who do sighted evaluations. One is riskier and more commonly invalid than the other. ;-)


QUOTE
2. Vinyl playback systems have a magnetic system that actually smooths over the choppiness of what can be considered gaps between the bit positions and samples.


Misapprehension number 3: There are no gaps between the samples in a digital file.

QUOTE
High quality DACs would have similar responses but as I have already discussed, most people do not use high quality DACs.


Obviously, you've never done anything technical with digital audio or done any studies of it based on credible sources.

I just gotta give you some friendly advice. There are some people around here get impatient with the intellectually lazy and the otherwise intellectually challenged.


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mjb2006
post Sep 3 2014, 05:07
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QUOTE (Arnold B. Krueger @ Sep 2 2014, 09:10) *
QUOTE
Your original question was what the sample rate and bit depth equivalents are for vinyl, and someone already accurately answered that it is 44k and 12 bit.


Oh, someone was being optimistic about vinyl?


The 12-bit number comes from digitally recording from a turntable (i.e., ripping vinyl). The recording software's peak meter shows that the noise floor, when the needle is playing an unmodulated part of the groove, hovers around something like 50 to 70 dB below peak, depending on I-don't-know-what. So that's why we say you need 10-12 bits or so, just to make sure you get everything above the noise floor. Really, though, that peak is dominated by the motor rumble and tonearm resonance. Roll off the EQ below 30 Hz and the peak drops quite a bit. What does this mean for the bit depth? Well, who knows. Maybe you need more bit depth. But then, music on vinyl generally is mastered as loud as possible to keep the SNR down, so maybe you need less.

Here's a recording I made of an unmodulated groove that takes up a whole side of a 12" record, for your analyzing pleasure: (click)
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lithopsian
post Sep 3 2014, 11:51
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QUOTE
Misapprehension number 3: There are no gaps between the samples in a digital file.

Well technically there are "gaps" between samples. That's kind of what a sample is, a specification of the waveform at a specific point, saying nothing about other points. The bit most people misunderstand is that samples at a particular interval represent only a single possible waveform (within the accuracy of the available bits and assuming a high frequency cutoff at half the sampling frequency). There are no "steps" as so often drawn to bamboozle the innocent, no possible output other than the one that was originally encoded to digital form.

To re-iterate, the output from even a modest DAC is *exact*, not a smoothed-over version of a series of jagged steps. This is why even cheap DACs produce high quality output. The only things "wrong" with the output are the filtered-out high frequencies and quantisation noise (almost always dithered to a low level general noise floor) from the discrete bit depth intervals.
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Arnold B. Kruege...
post Sep 3 2014, 19:15
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QUOTE (lithopsian @ Sep 3 2014, 06:51) *
QUOTE
Misapprehension number 3: There are no gaps between the samples in a digital file.

Well technically there are "gaps" between samples.


In what alternate universe?

QUOTE
That's kind of what a sample is, a specification of the waveform at a specific point, saying nothing about other points.


Not at all.

One of the prerequisites for proper sampling is low pass filtering the analog signal so that there are no components at or above the Nyquist frequency. That enforces a rule that says that all of the points between the samples are known quantities, which means that if you know the sample points you know everything about the other points.

Come on guy, this is digital audio 101, first few lectures if not the first lecture!


QUOTE
The bit most people misunderstand is that samples at a particular interval represent only a single possible waveform (within the accuracy of the available bits and assuming a high frequency cutoff at half the sampling frequency). There are no "steps" as so often drawn to bamboozle the innocent, no possible output other than the one that was originally encoded to digital form.


..and therefore no empty spaces with unknown data, no gaps at all.


QUOTE
To re-iterate, the output from even a modest DAC is *exact*, not a smoothed-over version of a series of jagged steps. This is why even cheap DACs produce high quality output.


Making that true is the responsibility of the low pass filter that is always on the output of a proper DAC.

QUOTE
The only things "wrong" with the output are the filtered-out high frequencies and quantisation noise (almost always dithered to a low level general noise floor) from the discrete bit depth intervals.


Thing is, those are all reducible to small amounts that vastly improve on anything that was ever done with analog recording of any kind.

Keeping analog signals pure enough for good digital processing is generally a challenge. It seems like every time someone comes out with a hot new ADC/DAC chip, they have to come up with an improved op amp to go with it.
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lithopsian
post Sep 3 2014, 19:45
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I wonder if you are being deliberately obtuse. Sampling is exactly the process of specifying the amplitude of a waveform only at particular points. By the process you describe, this is sufficient to mathematically reproduce the entire waveform (subject to the given caveats), but the samples are just that: individual points. Just because all the samples taken together are sufficient to reproduce the waveform does not mean that an individual sample has anything at all to say except at one particular time. The samples are required to be considered together in order to derive the state of the waveform in between each sample.

This post has been edited by lithopsian: Sep 3 2014, 20:12
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pdq
post Sep 3 2014, 20:18
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QUOTE (lithopsian @ Sep 3 2014, 14:45) *
I wonder if you are being deliberately obtuse. Sampling is exactly the process of specifying the amplitude of a waveform only at particular points. By the process you describe, this is sufficient to mathematically reproduce the entire waveform (subject to the given caveats), but the samples are just that: individual points. Just because all the samples taken together are sufficient to reproduce the waveform does not mean that an individual sample has anything at all to say except at one particular time. The samples are required to be considered together in order to derive the state of the waveform in between each sample.

I don't think that what you two are saying is that different. Yes, a sample represents a signal at an instant in time, but because the signal had been bandwidth-limited, the sample contains information from before and after that instant.
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audiophool
post Sep 3 2014, 21:41
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QUOTE (pdq @ Sep 3 2014, 21:18) *
I don't think that what you two are saying is that different. Yes, a sample represents a signal at an instant in time, but because the signal had been bandwidth-limited, the sample contains information from before and after that instant.

Isn't that beside the point? lithopsian was not talking about the information contained in samples.

I have a signal in continuous time. I sample it at various discrete points in time. I don't have a continuous function anymore.

I get that under certain conditions, the discrete samples are sufficient to recover the original continuous-time function, but that's an entirely different issue. It's still true that there is a gap -- a positive distance -- between any two points in time s =/= t at which the continuous-time signal has been sampled.

I am not in this field and maybe, I have the wrong metric in the back of my mind. Still, I find Arnold's way of talking about this very confusing.
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Green Marker
post Sep 3 2014, 21:52
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I think the average audiophile reading this would simply not 'get it'. Simply making statements that claim there are no gaps, when of course the audiophile knows there are, and mentioning low pass filters that the average audiophile equates with a turned-down treble control, is like a couple of old plumbers telling the new apprentice to go and get a glass hammer while winking at each other!

The average audiophile would need to be told that the filter at each end is not just any old low pass filter, but must have a specific mathematical response that ensures that what comes out at the far end is continuous and exactly like what went in i.e. that the 'digital bit' is only half of the system. The audiophile will benefit from being told that the filter does not just perform a linear-ish interpolation, but fills in *the gap* between digital samples with a precise curve that can exceed the amplitude of the adjacent samples.

It must be stressed that any experiences they've previously had with "8 bit audio" were probably on systems that did not use anything like the correct filters or dither. Many audiophiles will assume that the lowest 8 bits of their CDs sounds just like a Commodore 64 playing Manic Miner, and that going to 16 bits just hides that grunge a little lower down. They do not realise that 8 bit audio sounds just like 16 bit audio, but just a little noisier (not more distorted or 'crunchy').

It's all in the Xiph video, of course (which is great) but it is clear that some people miss vital points.

Once they understand all that, they can begin to appreciate how imprecise vinyl is, and how 12 bit equivalence seems very optimistic indeed.
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Kohlrabi
post Sep 4 2014, 00:02
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QUOTE (audiophool @ Sep 3 2014, 22:41) *
I get that under certain conditions, the discrete samples are sufficient to recover the original continuous-time function, but that's an entirely different issue. It's still true that there is a gap -- a positive distance -- between any two points in time s =/= t at which the continuous-time signal has been sampled.

I am not in this field and maybe, I have the wrong metric in the back of my mind. Still, I find Arnold's way of talking about this very confusing.
What Arnold says is that for a properly antialiased/low-passed sampled signal there is only one completely determined possible solution for the waveform, thus also the points between the sample points are determined. To quote:
QUOTE (Shannon)
If a function x(t) contains no frequencies higher than B cps, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.
Of course by low-passing you discarded any higher frequency information before, and you had to as a prerequisite, as is evident from the first part of the quote.

I think it's more helpful to go over to the frequency domain, and think of audio signals as oscillations with certain frequencies. After sampling with a low-pass filter, the recorded samples allow you to continuously reproduce all of the recorded oscillations/frequencies below half the sampling frequency. Now it should be pretty evident that there is no "gap", at least regarding frequency/information content. If you want to think in the time domain, the sampling frequency defines the time spacing or time "gaps" between the sample points. But the points in these gaps correspond to higher frequencies. Also, if you assume time is not quantised, it is impossible to sample "gaplessly". But as I quoted above, this is also unnecessary for reproduction of the (relevant, low-passed) information.

This post has been edited by Kohlrabi: Sep 4 2014, 01:13


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post Sep 4 2014, 05:45
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QUOTE (Kohlrabi @ Sep 4 2014, 00:02) *
QUOTE (audiophool @ Sep 3 2014, 22:41) *
I get that under certain conditions, the discrete samples are sufficient to recover the original continuous-time function, but that's an entirely different issue. It's still true that there is a gap -- a positive distance -- between any two points in time s =/= t at which the continuous-time signal has been sampled.

I am not in this field and maybe, I have the wrong metric in the back of my mind. Still, I find Arnold's way of talking about this very confusing.
What Arnold says is that for a properly antialiased/low-passed sampled signal there is only one completely determined possible solution for the waveform, thus also the points between the sample points are determined. To quote:
QUOTE (Shannon)
If a function x(t) contains no frequencies higher than B cps, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.
Of course by low-passing you discarded any higher frequency information before, and you had to as a prerequisite, as is evident from the first part of the quote.

I think it's more helpful to go over to the frequency domain, and think of audio signals as oscillations with certain frequencies. After sampling with a low-pass filter, the recorded samples allow you to continuously reproduce all of the recorded oscillations/frequencies below half the sampling frequency. Now it should be pretty evident that there is no "gap", at least regarding frequency/information content. If you want to think in the time domain, the sampling frequency defines the time spacing or time "gaps" between the sample points. But the points in these gaps correspond to higher frequencies. Also, if you assume time is not quantised, it is impossible to sample "gaplessly". But as I quoted above, this is also unnecessary for reproduction of the (relevant, low-passed) information.

Who is this explanation for? If it is for an engineer or a mathematician then they probably know it already. If it is for a curious audiophile who understands how a needle tracks a wiggly groove, but has suspicions about how digital audio can achieve the same thing, then you are losing him at "frequency domain".... "Shannon"... "information theory"....a function x(t)"...

This chasm in understanding is where the myths and superstitions about digital audio have crept in.
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mjb2006
post Sep 4 2014, 06:12
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You hit the nail on the head. In the typical audiophile's view, there's just no way that samples can represent whatever the waveform is doing in between the sample points, unless the waveform just happens to be that one specific, tight curve. "What if the waveform is all squiggly in between the sample points? What if it's a square wave?"

What needs to be demonstrated is that the filter removing the frequencies above the Nyquist removes the between-sample squiggles such that the samples do represent this smoothed-out curve perfectly, and that this smoothing doesn't result in any crucial information being lost. Thus, those squiggles weren't contributing anything to the frequency components below the Nyquist. (That's right, right?)

IIRC, Monty's video shows some of this, but relies too much on his calm reassurances rather than a demo of every step of the process, both in simple terms and with a real-world example.

This post has been edited by mjb2006: Sep 4 2014, 06:20
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Kohlrabi
post Sep 4 2014, 09:18
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QUOTE (Green Marker @ Sep 4 2014, 06:45) *
Who is this explanation for? If it is for an engineer or a mathematician then they probably know it already. If it is for a curious audiophile who understands how a needle tracks a wiggly groove, but has suspicions about how digital audio can achieve the same thing, then you are losing him at "frequency domain".... "Shannon"... "information theory"....a function x(t)"...

This chasm in understanding is where the myths and superstitions about digital audio have crept in.
By the way, in the following, when I say 'you' I mean the general 'you', not you, Green Marker:

I'm sorry, but if someone decides to talk about audio, signal processing and so forth I expect him to do some basic research himself. There are a vast amount of sources on the net to read up on this. This is as easy as it gets, beyond going out on a limb and giving a lecture on these matters. If someone chooses to be ignorant about these matters it's fine by me, but he should show a little dignity and please just stop talking about it. If you want to stay a child and expect that others spoon-feed you your information you should stay away from grown-up discussions. It's nobody's job here to teach, but some of us are really doing some steps towards the uninitiated.

QUOTE (mjb2006 @ Sep 4 2014, 07:12) *
What needs to be demonstrated is that the filter removing the frequencies above the Nyquist removes the between-sample squiggles such that the samples do represent this smoothed-out curve perfectly, and that this smoothing doesn't result in any crucial information being lost. Thus, those squiggles weren't contributing anything to the frequency components below the Nyquist. (That's right, right?)
Why does it "need to be demonstrated"? It has been shown and it's inside the mathematics and the explanations of the Shannon-Nyquist theorem. What needs to be done is that people who claim something back that up with evidence and at least acknowledge current scientific knowledge. We aren't all experts in these matters (I'm very far from it), but it's common discussion "rule" to back up or demonstrate some knowledge about the topics you talk about. Contrary to politics, art, and entertainment topics here are not only a matter of opinion.

This post has been edited by Kohlrabi: Sep 4 2014, 09:31


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2Bdecided
post Sep 4 2014, 10:05
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Here is the process:

1. pick a sampling frequency
2. input signal
3. remove everything above half that sampling frequency using a filter
4. do your fancy digital sampling at that sampling frequency
5. remove everything above half the sampling frequency using a filter
6. output signal

No one says the input signal equals the output signal. There's two filters in there. They change the signal.

However, what is mathematically proven with as much certainty as 2+2=4 is that as long as you have stages 3 and 5, stage 4 makes absolutely no difference. Its presence or absence from the process is completely undetectable at the output. Take a while to understand that. It's pretty fundamental.

Sampling does not change the output if the right filters are in place.

Hence what matters, both in theory and in practice, is not sampling but filtering.

It is possible to design and realise (in the real world) a filter that will remove everything above half the sampling frequency to as good an accuracy as you want. The stuff you don't want can be made 180dB lower than the stuff you do want. That's a change equivalent to taking something that's as loud as a jet engine next to you, and reducing it so much that it becomes inaudible even in the quietest room on the planet. Hence the requirement to "remove" the frequencies above half the sampling frequency has been met.

You're left with only one potentially audible issue: did the filter (actually, both filters in series) mess up something that you can hear? It is possible to design and realise (in the real world) a filter that doesn't even touch anything below half the sampling frequency, again to as good an accuracy as you want. Any "faults" can again be made 180dB lower than the loudest signal. For all intents and purposes they just don't exist. It's better than the purest piece of wire you can imagine.

Up to a given frequency, it's perfect. Beyond that frequency, everything from the original signal has gone. Some people are concerned about the hard transition between those two states (at about 22kHz for CD audio), but you can soften the transition without breaking anything, as long as you soften it downwards.

Again, the question isn't about sampling. It's about filtering. Can you hear a filter that removes everything above 22kHz?

Cheers,
David.
P.S. there's quantisation too. wink.gif
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2Bdecided
post Sep 4 2014, 10:12
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QUOTE (mjb2006 @ Sep 4 2014, 06:12) *
What needs to be demonstrated is that the filter removing the frequencies above the Nyquist removes the between-sample squiggles such that the samples do represent this smoothed-out curve perfectly, and that this smoothing doesn't result in any crucial information being lost. Thus, those squiggles weren't contributing anything to the frequency components below the Nyquist. (That's right, right?)

IIRC, Monty's video shows some of this, but relies too much on his calm reassurances rather than a demo of every step of the process, both in simple terms and with a real-world example.
Monty's video includes exactly this from about 4 minutes in...
http://xiph.org/video/vid2.shtml
...showing exactly what you want from about 5 minutes with high frequency sine waves. Square waves at 17:50.

Good enough?

Cheers,
David.

This post has been edited by 2Bdecided: Sep 4 2014, 10:21
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