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Author Topic: George....what's the resolution of analog?  (Read 88472 times)

Nika Aldrich

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Re: George....what's the resolution of analog?
« Reply #45 on: May 16, 2004, 02:05:20 pm »

David,

It's a good attempt.  Allow me to throw in some corrections below.

dwoz wrote on Sun, 16 May 2004 18:35



when an analog signal is sampled, it is essentially 'sliced' into segments, each of which has a certain width in time.


No.  The samples have no "width" in time at all.  They are momentary and instantaneous samples of the amplitude of the waveform at moments in time and do not imply what comes before or after them.  Only on a computer screen are we led to think that the samples have width, because a computer screen tries to draw it up there in a way that is pleasing to the eye.  In reality, sample points should be given to us as mere dots in space with no connecting line between them at all.  That would help drive home the point that the samples are infinitely short in time.

Quote:

These 'slices' have to be made small enough that the signal being sampled cannot change direction TWICE inside the slice. (that's the nyquist thingy).  Another way of saying this is that the frequency of the signal must be limited so it CAN'T go south then north inside a single slice.


More complicated than just going north and then south between two samples.  Higher frequency content doesn't always manifest itself like that.  Higher frequency content also causes steep angles and corners and much more.  All of those behaviors are illegal also.  Trying to adhere to Nyquist by means of discussing movement between samples implies a degree of misunderstanding about the genius of Nyquist and the role of reconstruction filters.  

Quote:

OK, so when we check the voltage of this sample, we really have to make TWO measurements...the absolute level, and also the slope of the wave. without these two, we don't really know the complete behavior of that signal. But the measure we take is only the level.  BUT, because of the definition we've given, that the signal will only go up, or go down, or go up and down ONCE within the sample, we can check the samples on either side and infer a slope for the width of the sample.  It isn't perfect, but its pretty much good enough for our purposes.


No no no, and this is the dangerous part that people are led to believe.  This is also the beauty of Nyquist.  Nyquist came forth with a radical theory that you can know only ONE piece of information in order to completely accurately reconstruct the waveform, and that one piece is the amplitude at regular intervals of time.  With a little trick math the ENTIRE rest of the waveform can be 100% of the waveform can be entirely and accurately reconstructed with proper amplitude, frequencies, and phase.  In other words, we don't need to know the slope!!  If we know only the amplitude of regular intervals Nyquist tells us that we can figure out the slope.  You must admit that this is a pretty revolutionary concept - one that defies common logic and simple intuition.  And THAT is why it took over 20 years before a mathematician proved Nyquist correct.

So the point is that digital audio is not at all imperfect as you imply because we have all the information needed to reconstruct the waveform.

Quote:

What we're talking about here is QUANTIZATION ERROR.  by knowing both the absolute value of the sample (either the leading edge, the exact middle, or the tail edge) and the interpolated slope, we can make some pretty good guesses about what "number" we should put in the output stream, so our DAC can reconstruct an analog signal that is very much like our input.


I'm not following this yet but I don't believe you're on the right path?  Quantization error is only the error yielded by having to round the sample up or down to the latest quantization step when we take the sample.

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So, the sample rate controls HOW WIDE (or long) that sample is in time.


Semantical correction - it controls HOW OFTEN the samples are taken, not how wide the samples are.

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The bit depth controls how fine the discrete measurements we can make can be accurately captured.  If we're trying to represent the whole dynamic range of the signal with just 8 bits, then we have to make some pretty gross approximations of the value of the particular we just measured. If we're using 28 bits, then the chance that the EXACT value of the sample that we just measured is only a tiny bit off a discrete integer that we can record, is much better.


Right!

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It should be obvious that BOTH the sample rate, and the bit rate, contribute to the QUANTIZATION ERROR.


Absolutely not!!!  Only the bit depth relates to quantization error.  Sample rate is completely unrelated.

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If I have a very high sample rate, then the more likely that my measurement of the slope is close to the actual value. I can rely on the absolute value of the sample, and less on the slope...and the higher the bit depth, the closer the measured value will be to one I can record.  Remember, I have to round any 'inbetween' floating point value to an integer.


no, no, no, as I explained above.

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So, resolution of digital signals is dependent on both the sample rate, and the bit depth, to some extent.


Errr...language like this is specious and not the most descriptive way to describe what is happening.  

Quote:

In the context of what I've just said, the "resolution" of analog signals would be to all intents and purposes, infinite. Not REALLY infinite of course, and when I can count individual electrons and quanta, then we can enter that discussion of just HOW INFINITE it is.


Again, not the best way to describe, for it denies the reduction in accuracy on the analog signal due to added noise and distortion.  Since digital signals add less noise and distortion it is hardly accurate to say that analog signals have more "resolution," and is one of the reasons why it is best to shy away from that term - it does not do an accurate job of communicating anything pertinent about waveforms.  While one can look at dictionary definitions and find that the term is theoretically relevant, it is actually quite inappropriate and doesn't adequately describe useful information in the context of analog vs. digital recordings.

Nika.
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dwoz

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Re: George....what's the resolution of analog?
« Reply #46 on: May 16, 2004, 02:26:39 pm »

I don't agree that noise is a limiter of resolution.  I find that to be a red herring.  Of course noise is a factor, but as many others have noted, and as many including myself have heard time and time again, content can be discerned under the noise floor.

Noise is never good, but noise floor isn't necessarily a boundary.


also, I completely understand that a sample is an instant, without width...thus my "leading edge, middle, trailing edge" qualification of the "width" of a sample.  the sample represents a choice of a single value among perhaps many inside the span of time being represented by that sample.

I stand by my assertion that sample rate has to do with quantization error...as the more time between samples, the more opportunity to pick a value that doesn't represent the activity within the sample.  I definitely grant to you the point that bit depth has more effect on quantization error, perhaps by an order of magnitude or more, but still it IS A FACTOR.


And again, I stated that we only record the absolute value, not the slope, because we can interpolate slope using adjacent values, not having to resort to "complex" calculus and defining slope and value....as you state, after all, that because of nyquist, we don't see real values of slopes that diverge significantly from our ability to interpolate their values.


thanks for your reply.

dwoz
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dwoz

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Re: George....what's the resolution of analog?
« Reply #47 on: May 16, 2004, 02:31:10 pm »



Another thing....


ANALOG RESOLUTION.   I suppose that a 1/2" 2 track tape that is capable of slurping up +18db peaks, would "beat" a cassette deck running 1/16" track width that can barely manage -10db levels?

Or, a board with 24volt rails, compared to one with 12 volt rails...being able to pass +24db signal without mangling it, compared to one that decapitates a +12db signal as a matter of course?

Is there fodder for discussion there?

dwoz
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sfdennis

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Re: George....what's the resolution of analog?
« Reply #48 on: May 16, 2004, 02:50:51 pm »

Charles, I just had to retract this post. It was all wet. -Dennis
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Jim Dugger

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Re: George....what's the resolution of analog?
« Reply #49 on: May 16, 2004, 04:35:39 pm »

dwoz wrote on Sun, 16 May 2004 13:26

I stand by my assertion that sample rate has to do with quantization error...


May I ask Nika or one of the others here to help explain something to me in clearer (layman) terms?

It is true that the time and frequency domain are quite linked, correct?  Afterall, there are well known ways to covert information of one kind into the other.

So, does it stand that increasing the sampling rate is somehow (within some reasonable limits) equal to adding one bit to the frequency domain?

In other words, is a signal, optimally represented at 16/88.2, essentially equal to a signal optimally represented at 17/44.1?  You may assume the signal not to contain out-of-bandwidth information.

If not, where in the system of A2D, DSP then D2A do the time/frequency domain correlations break down?  Or, did they never exist at all, and are only available using math on already digital signals?

The answer may help several pieces of stone presently rattling around in my head come together...

--Jim
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Bill Mueller

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Re: George....what's the resolution of analog?
« Reply #50 on: May 16, 2004, 07:56:20 pm »

dwoz,

I'm not sure by your post if you were answering me regarding noise being a limiting factor to resolution, however if we define resolution as fidelity (the truest possible conversion of an acoustic event) then noise is a limiting factor. Any signal coming out of a device that is not present at the input, limits fidelity.

I absolutely agree that signal can be heard below noise in an analog system. If the signal is at a different frequency than the noise, then it can be heard even better. This is called the masking effect. If I recall, the masking effect works down to about 6 db below signal, meaning that you can hear signal about 6 db below noise if that noise is present at that frequency. If anyone has better figures here I would appreciate it.

To me analog noise is sort of like digital bit depth in its affect on the signal. While you can hear low level signal in both analog and digital systems, they are each distorted by the medium.

Many don't seem to realize that recordings made 6 db below clip on digital systems, result in one less bit than maximum, ie -6 db on a 16 bit system results in a 15 bit (1/2 resolution) recording, -12 db results in a 14 bit recording (1/2 resolution of the 15 bit recording) and so on. Therefor as you fade out a signal, the resolution drops precipitously. Crank up your fades sometime for a truly horible experience.

A similar thing happens in analog except that to my ear, it sounds significantly better.

Best regards,

Bill
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Zoesch

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Re: George....what's the resolution of analog?
« Reply #51 on: May 16, 2004, 09:36:19 pm »

Bill Mueller wrote on Mon, 17 May 2004 09:56

dwoz,

I'm not sure by your post if you were answering me regarding noise being a limiting factor to resolution, however if we define resolution as fidelity (the truest possible conversion of an acoustic event) then noise is a limiting factor. Any signal coming out of a device that is not present at the input, limits fidelity.


Resolution is your ability to resolve, noise does indeed limit what you can resolve due to masking, but it doesn't really change your measurement resolution.

Quote:


To me analog noise is sort of like digital bit depth in its affect on the signal. While you can hear low level signal in both analog and digital systems, they are each distorted by the medium.


I don't follow this... the noise floor has an effect on headroom, say if you calibrate your A/D chain to reach 0dBFS exactly when you top in headroom then yes, analog noise will definitely have an effect on how well you can convert the signal, the lower the noise the more precise your sampling would be at lower levels.

Quote:


Many don't seem to realize that recordings made 6 db below clip on digital systems, result in one less bit than maximum, ie -6 db on a 16 bit system results in a 15 bit (1/2 resolution) recording, -12 db results in a 14 bit recording (1/2 resolution of the 15 bit recording) and so on. Therefor as you fade out a signal, the resolution drops precipitously. Crank up your fades sometime for a truly horible experience.



Yep, we all know the beauties of hard bound linear systems... that's why that BS about recording hot to digital was so wrong, but it was perpetuated around without people questioning it. Then you need to take into account how summing is implemented in your DAW of choice, but that is for another (presumably lenghty) debate.

Quote:


A similar thing happens in analog except that to my ear, it sounds significantly better.



Simply because in the analog domain the transfer curves aren't fully linear, so at high gain you are compressing the signal. And, the signal you clip once you run out of headroom has a more balanced content of odd and even harmonics as opposed to a hard-clipped digital signal which contains mainly odd harmonics.

A good designed system should avoid that, but again that's been debated 'till kingdom come, and some people are quite religious about their DAWs.
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hollywood_steve

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Re: George....what's the resolution of analog?
« Reply #52 on: May 16, 2004, 10:20:46 pm »

All of the gear used today beats all of the gear used years ago in every way you care to assess gear. But the rooms have gotten much smaller, and a lack of proper acoustic treatment compounds the problem.

That first sentence is a loaded statement that shouldn't pass without comment.  

every way you care to assess gear

the only way that really matters is how it sounds.  And I'll take the SOUND of classic analog gear any day, and so will a lot of people who might think otherwise.

for example, I'll take

mics: a pair of (you choose: Neumann u47/48/M49/M50, RCA 44/77d, AKG c12 / Telefunken 251, among others)

console:  API 1604 or EMI REDD37

recorder: Studer A800 1" 8trk and Ampex ATR102 2trk

in any room at any time against the best of 2004 (and there is some AMAZING gear made by some small companies these days).  At some point the only "improvements" are discerned by test equipment.  I'm not the only one who thinks the best analog gear of the 70s was already as good as gear needed to be; it was just too expensive for all but the best studios. All we've done since then is made decent gear available to the masses; unfortunately, at the same time we have lowered the bar for what passes as acceptable commercial "product."



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Brent Handy

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Re: George....what's the resolution of analog?
« Reply #53 on: May 16, 2004, 10:44:04 pm »

Chuck wrote on Sat, 15 May 2004 17:43

Former Oceanway drone wrote on Sat, 15 May 2004 17:17


I certainly have opinions about analog vs. digital and I have no intention of talking about them right now. That said, I do have a problem with Chuck's connecting the declining recording quality of Eagles albums with a "decline" in analog.



Hi Alan,,

thanks for filling in the info on recording gear and engineers.

Of course there are great recordings being made after the 70's.

I did not want to say that available analog equipment is getting worse over time.

But in general terms, while cruising through my record collection, I am expecting good sound from late 60's to late 70's some to '82, then it appears to become increasingly difficult to obtain that rich hi-fidelity sound quality.

Btw. I also have the early Eagles records on CD with a sticker on them that says:"digitally remastered", and if you know and have the records, I would say the CDs are just unlistenable.

I don't blame it on digital or the CD format. But actually, I don't know who or what I would want to blame for it. For me, subjectively, it is just a decline in audio quality.

I have Joni Mitchell Hejira on vinyl, and I have the Travelogue album on CD. Both excellent, really very very good.

Lately I bought Joni Mitchell 'Both sides now' as 24/96 DVD-A. As I have Chesky 24/96 DVDs that are really excellent, I expected something.

But the Joni Mitchel DVD-A sounds like crap. I read the names Geoff Foster, Allen Sides and Bernie Grundman on the inlet. I don't know these guys personally, maybe you know them...

I have just no comprehension and no words for the decline in audio quality, that I have to face today.

I just wonder: "How did they manage to have that wonderful sound, almost half a century ago, and what are the reasons, that make it so difficult to achieve today ?"

Charles Smile


And to think that all those great, flat records were mixed and monitored on those  JBL 4311's and the like.  What a testament to fine skill.

This is what blows me away about people critiquing other's work.  Maybe, just maybe the artist/engineer wanted the result that you hear?  Maybe your hearing is jaded by the romance (or lack there of) of a particluar time in your life.  Or maybe, that your "crap" sound from the LP's might be related to the mastering/pressing from a record club, etc.

I have listened to records from my youth, and remember them being much better than what they actually sound.  Granted CD's do sound different than records, and you don't get the words that you can read without a magnifying glass, the cool artwork, and the smell of vinyl. I don't know about you, but I gave up the Grado turntable long ago.  I enjoy pop free, rumble free, scratch free music.  What I like best is that I can get 10x in the peach crates. LOL
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Zoesch

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Re: George....what's the resolution of analog?
« Reply #54 on: May 16, 2004, 11:37:25 pm »

hollywood_steve wrote on Mon, 17 May 2004 12:20

the only way that really matters is how it sounds.  And I'll take the SOUND of classic analog gear any day, and so will a lot of people who might think otherwise.

for example, I'll take

mics: a pair of (you choose: Neumann u47/48/M49/M50, RCA 44/77d, AKG c12 / Telefunken 251, among others)

console:  API 1604 or EMI REDD37

recorder: Studer A800 1" 8trk and Ampex ATR102 2trk

in any room at any time against the best of 2004 (and there is some AMAZING gear made by some small companies these days).  At some point the only "improvements" are discerned by test equipment.  I'm not the only one who thinks the best analog gear of the 70s was already as good as gear needed to be; it was just too expensive for all but the best studios. All we've done since then is made decent gear available to the masses; unfortunately, at the same time we have lowered the bar for what passes as acceptable commercial "product."






I think you are right from the sonics point of view, there was of course very good equipment made in the 80's and 90's (Mainly FX boxes) but when it came down to consoles I think the late 70's and early 80's produced the best designs of them all.

One problem though, although it'd make sense for analog consoles to have become cheaper over time, the reality is, good designs are hard to manufacture and require extensive design resources, most mass produced consoles tend to sound bad just because they were designed with cheap and quick manufacturing in mind,
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oudplayer

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Re: George....what's the resolution of analog?
« Reply #55 on: May 17, 2004, 02:13:55 am »

Ethan Winer wrote on Sun, 16 May 2004 09:41

Charles,

> How did they manage to have that wonderful sound, almost half a century ago, and what are the reasons, that make it so difficult to achieve today? <

Years ago music was recorded and mixed in real recording studios that had large rooms. The better studios also had sufficient bass trapping and other acoustic treatment so the recordings were not permeated with the "small room" sound we hear so much today. And the mix engineers were able to hear what they were doing much more accurately than folks today who work in small untreated bedrooms.


I don't believe that a comparison of today's bedrooms and yesteryear's top-flight studios is reasonable. There are many people that are a part of this discussion (myself included) who regularly work in quite large recording facilities, in amply-sized concert halls, and basically in spaces that are no larger nor smaller than those of yesteryear. Working in those spaces one doesn't "automatically" get that sound of half a century ago.

Quote:


All of the gear used today beats all of the gear used years ago in every way you care to assess gear. But the rooms have gotten much smaller, and a lack of proper acoustic treatment compounds the problem.



I entirely, thoroughly disagree. The way current digital gear offerings handle overs is entirely ungraceful and destroys the data thoroughly. Digital gear may offer certain kinds of fidelity or precision during "optimum use," but until it is implemented in a way that matches the kinds of quick decision-making and equipment adjustment that characterize certain active recording and mixing techniques, it doesn't integrate uniformly into many recording workflows. I think this may change with new products and a different design philosophy, but until then...

You can design a hand saw that makes the most incredibly precise cut when cutting strictly with the grain, but that totally destroys the piece of wood when used at a slight angle across grain. Is this a better saw? Sometimes we need to cut across the grain - the new hand saw is not the tool for all jobs.

-eliot bates
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oudplayer

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Re: George....what's the resolution of analog?
« Reply #56 on: May 17, 2004, 02:20:01 am »

Brent wrote on Sun, 16 May 2004 19:44

I have listened to records from my youth, and remember them being much better than what they actually sound.  Granted CD's do sound different than records, and you don't get the words that you can read without a magnifying glass, the cool artwork, and the smell of vinyl. I don't know about you, but I gave up the Grado turntable long ago.  I enjoy pop free, rumble free, scratch free music.  What I like best is that I can get 10x in the peach crates. LOL


I have a good-sized collection of orchestral, Chinese, and Armenian music on 78s - the pops and rumble do not at all get in the way of my enjoyment of the music. And nothing made today sounds like it (with the exception of the 78s that the Cheap Suit Serenaders released a few years back). Not that they're the best sonics - obviously the dynamic range is, like, 10dB, and the frequency response... you can count it on one hand. But the effect of the recording focuses your attention on certain aspects of the music - the effect of modern CDs is entirely different.
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davidc

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Re: George....what's the resolution of analog?
« Reply #57 on: May 17, 2004, 04:09:59 am »

oudplayer wrote on Mon, 17 May 2004 07:20

I have a good-sized collection of orchestral, Chinese, and Armenian music on 78s - the pops and rumble do not at all get in the way of my enjoyment of the music. And nothing made today sounds like it (with the exception of the 78s that the Cheap Suit Serenaders released a few years back). Not that they're the best sonics - obviously the dynamic range is, like, 10dB, and the frequency response... you can count it on one hand. But the effect of the recording focuses your attention on certain aspects of the music - the effect of modern CDs is entirely different.


I agree with you completely, oudplayer. It is not the resolution, or clarity that makes great music amazing to listen to. Do you think that higher resolution digital formats are any better in this regard?

I think that it is erroneous to think that analog tape has distortion (pleasing never the less), whilst digital is accurate. Digital has all kinds of distortions, that are not as well understood, and can have the effect of lowering the musical impact.

Best Regards

David C
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Nika Aldrich

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Re: George....what's the resolution of analog?
« Reply #58 on: May 17, 2004, 10:04:38 am »

dwoz wrote on Sun, 16 May 2004 19:26

I don't agree that noise is a limiter of resolution.  I find that to be a red herring.  Of course noise is a factor, but as many others have noted, and as many including myself have heard time and time again, content can be discerned under the noise floor.


Yes.  The noise floor is not the bottom of hearing ability, but it marks the bottom.  Humans can hear generally about 20dB below the noise floor under ideal conditions, and mathematical proof has that amount limited to something like 30dB.  Thus, the level of noise is still the arbiting factor of dynamic range (what some choose to call "resolution") though the actual value is 20dB to 30dB lower than that, though heavily dependant upon signal content and other conditions (like the amplitude of the signal).

Quote:

Noise is never good, but noise floor isn't necessarily a boundary.


It marks the boundary and indicates where it is.


Quote:

also, I completely understand that a sample is an instant, without width...thus my "leading edge, middle, trailing edge" qualification of the "width" of a sample.  the sample represents a choice of a single value among perhaps many inside the span of time being represented by that sample.


No.  The sample represents the amplitude at an infinitely small moment in time which is at an equal distance from the last sample and the next sample.

Quote:

I stand by my assertion that sample rate has to do with quantization error...


You may stand by this but it is absolutely erroneous.  Sample rate has absolutely nothing to do with quantization error.  Ask about it and I will explain but I'm not sure what allows you to draw this assessment as of yet.

Quote:

as the more time between samples, the more opportunity to pick a value that doesn't represent the activity within the sample.


Totally lost on this phrase.  There is no "picking" of samples.  At the moment a sample is to be taken a sample is taken.  I don't get your phrase "activity within the sample?"

Quote:

And again, I stated that we only record the absolute value, not the slope, because we can interpolate slope using adjacent values, not having to resort to "complex" calculus and defining slope and value....as you state, after all, that because of nyquist, we don't see real values of slopes that diverge significantly from our ability to interpolate their values.


We don't see ANY values of slopes that diverge, because Nyquist's data is enough to completely reconstruct the waveform with 100% accuracy.

Trying to help - let me know where I'm breaking down in communication.

Nika.
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Nika Aldrich

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Re: George....what's the resolution of analog?
« Reply #59 on: May 17, 2004, 10:17:23 am »

Jim Dugger wrote on Sun, 16 May 2004 21:35


May I ask Nika or one of the others here to help explain something to me in clearer (layman) terms?


I will try.

Quote:

It is true that the time and frequency domain are quite linked, correct?  Afterall, there are well known ways to covert information of one kind into the other.

So, does it stand that increasing the sampling rate is somehow (within some reasonable limits) equal to adding one bit to the frequency domain?


Yes.  This is correct.  Remember that the sampling process adds error (we call it "quantization error") to the signal at an amplitude that is determinable by the bit depth.  In a 1 bit signal the error amplitude is -6dBFS.  For a 16 bit signal it is -96dBFS, etc.  That noise level is, for the sake of this discussion, white noise covering the range between DC and Nyquist.  So let's take a 16 bit 48KS/s situation for starters.  We have a noise floor in there that exists at a level of -96dB and covers the range of OHz to 24KHz.  

If we increase the sample rate to 96KS/s then the noise is now -96dB from 0Hz to 48KHz.  We know that white noise is equal amplitude at all frequency bands, so half of the noise is present from 0Hz to 24KHz, and the other half of the noise there is present from 24KHz to 48KHz.  Half of the noise amplitude is equivalent to lowering the noise 3dB.  Since the broadband noise is -96dB, each half of the range only has noise at -99dBFS.  In otherwords, with a 16 bit 96KS/s signal the noise from 0Hz to 24KHz is -99dBFS and the noise from 24KHz to 48KHz is -99dBFS, and when you add the two together the total noise from 0Hz to 48KHz is -96dBFS (double the noise, add 3dB).  

Notice that when we doubled the sample rate from 48KS/s to 96KS/s the noise in the audible range lowered by 3dB even though the broadband noise level stayed at the same amount (-96dBFS).  This is how doubling the sample rate can effectively lower the audible noise.  It is not that doubling the sample rate lowers the total noise level, but it instead spreads it across a wider range so that the audible noise level is reduced.  If you double the sample rate twice then you increase the audible dynamic range by 6dB, or 1 bit's worth.  So going from 48KS/s to 192KS/s does, in theory, increase your dynamic range by 1 bit, but with today's converters this is mitigated in other ways.  Further, with 24 bit protocols it is irrelevant as the bit depth already exceeds the dynamic range we can hear.

Nika.
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