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Author Topic: George....what's the resolution of analog?  (Read 59778 times)

Han S.

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Re: George....what's the resolution of analog?
« Reply #30 on: May 15, 2004, 05:34:13 pm »

Quote:

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


That's a very good point and it makes me wonder as well.
In the late 50's there wasn't any multitrack, just two tracks and some recordings of that era sound much better than anything of today. Musta been the engineers (like Bill Putnam sr).
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Brent Handy

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Re: George....what's the resolution of analog?
« Reply #31 on: May 15, 2004, 06:08:10 pm »

My World wrote on Sat, 15 May 2004 03:13

I have been "begging" sound processing companies for several years to develop 28-bit processors!  C'mon guys!


I believe that there is a 28-bit processor.  But it is not a true usable 28-bit any more than a 24 is really 24.

Lets say that they get to 32, so that it performs at 28.  Will the microphones used to record hinder the process?
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Phillip Graham

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Re: George....what's the resolution of analog?
« Reply #32 on: May 15, 2004, 10:20:18 pm »

jazzius wrote on Fri, 14 May 2004 12:56

George, we hear about the resolution of digital all the time.....24 bits, 44.1, 192.....2.8 million whatevers....

...do you know if anyone has ever worked out the resolution of analog?.....how many bits would it be equivelent to?.....i know this is bit of a strange question, but i'd love to be able to give my customers a smart-arse answer for why analog sounds better then digital...

...cheers.....Darius


Hello Darius,

I am going to attempt to answer your original question, since this thread has nearly as much erronius information as the entire 192khz thread.  I think you will find this post far reaching, and hopefully educational.

Let's start by trying to define "resolution."  A common definition for this in physics is the Ralyeigh limit for optical "resolution."  It is approximately equal to .66*lambda.  It says that two objects closer together than .66*wavelength cannot be focused on well enough to tell one from the other.

In some sense the Nyquist frequency can be thought of as the limit of the (frequency,wavelength,length-however you want to look at it) "resolution" of a discrete time system.  Below the nyquist frequency all waveform content is completely captured, and above the nyquist frequency it aliases back into the lower frequencies (an erronius result).

It is important to understand that there is a difference between "discrete time" systems and "digital" systems.  Quantitization is a completely separate process from discrete time sampling.

Your ADC takes an "analog" voltage measurement at each sample, and then represents that as digital word of given length.  The longer the world length, the greater the difference in level between the quietest and loudest sounds.  You could view this differential as a measure of "resolution" if you wanted.

In the ancient world, Descarte proposed that the number line was continuous, a revolutionary idea.  But, as science and math progressed, many situations where discrete solutions, and phenomena, were observed.

So, with that in mind, we now shift to some physics behind "analog" electronics.

The fundamental magnetic moment observable in the known universe is that of an electron.  This number is known as the Bohr Magneton, and its value is 9.27x10-24 Joules/Tesla.

Materials used for magnetic properties have varying degrees of unpaired electrons, and the orientation of the quantum "spin" of these electrons eventually determines on a macroscale the magnetic behavior involved.  The formation of magnetic domains is the topic of full books.  I personally recommend the classic "Physical Properties of Crystals: Their Representation by Tensors and Matrices" by J. F. Nye.

The formation of magnetic domains is a dissipative and nonlinear process.  This can be represented by a hysteresis loop.  This hysteresis loop shows the nonlinear behavior of the magnetic media with applied field.  The positive portion of the curve looks something like the compressor curve you would draw in a DAW.  They do form a complete loop, though, and the volume of the center of the loop tells you how much energy was lost in the whole write/unwrite process.

While there are other magnetic responses (magnetoresistance for example), I believe the analog tape recorders of the recording world used simple induction to read and write their data.  A similar "read/write" process is the process of transferring the magnetic field from the primary of a guitar amplifier output transformer to the secondary, coupled by a magnetizable core material.  The nonlinear nature of the hysteresis curve gives much of the warm gooeyness of the analog medium.

I am tempted to talk about other subjects, such as electron thermalization, johnson noise, etc. but I don't want to devote further time to this before I see if it is heading in the direction you were looking to comprehend.
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Phillip Graham

jackpine

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Re: George....what's the resolution of analog?
« Reply #33 on: May 15, 2004, 11:07:36 pm »

 He took the words right out of my mouth. Razz
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Zack Reinig

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Re: George....what's the resolution of analog?
« Reply #34 on: May 16, 2004, 12:49:32 am »

I think what darius was referring to as 'better' is the three dimensional throw of analog (resulting from frequency dependent tape compression effect on transients) vs. the flat 2 dimensional feel of digital, and the lack of the easily audible distorted high end above 8k you can hear in straight digital 2 track mixes (even thru fantastic converters).  In my opinion, analog sounds more life like at times due to the same sort of distortion that occurs when the human ear is subject to overbearing spl (drum kit being played).
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jazzius

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Re: George....what's the resolution of analog?
« Reply #35 on: May 16, 2004, 03:48:03 am »

Thanks Phill......yeah, that's more what i meant....i wasn't asking about how well analog can be captured in the digital domain....only about the resolution of analog itself....looks like you're the only one who got it!.....i'm afraid most of what you wrote flew over my head but it was an interesting read, anyway!.....cheers!

Chuck

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Re: analog = magnetic filed ; digital = square
« Reply #36 on: May 16, 2004, 08:29:43 am »

chrisj wrote on Sat, 15 May 2004 20:40


There are no squares, really. You're looking at the visual representation of a bunch of numbers designed to tell the converter what kind of SINES to put out.
The only time you'd be hearing squares is if you were using one of those funky DACs with no reconstruction filter. And that's actually not technically correct, though there are some things about it that count as advantages...
The squares you're thinking of, you might be better served by thinking of them as lists of numbers, not as a waveform. Nothing is ever about trying to present that information as squares. The DAC wants to present it as sines again, that's what it's for. That's what a reconstruction filter is for.
What you should be looking into is not 'squares', not increasing frequency range (necessarily), but the types of harmonic and inharmonic distortion generated by each kind of recording.



Hi Chris,,

yes, I'm a funky guy with funky converters that put out funky squares that one may find many different ways in interpreting them into funky sines.

http://amm.haan.de/pn/0-ovs.jpg

In the pic I have used a not-so-good audio transformer, and tuned the circuit to ring a little at fs (in this case 44.1kHz). What you see on the top trace is the "filtered output". This is a very good sounding filter. The only problem is to get those bad transformers. With good transformers it don't work right...

You may think that modern DACs don't work with squares, because at the output you see sines plus noise, but they do. And the noise at the output are the HF residuum of the square-filtering-process.

By increasing the sampling frequency we get more but smaller squares. Oversampling does the same, except that the smaller squares are invented in between the real samples.

It is easier to filter small amplitude squares and on the other hand almost impossible to filter a 1-bit signal - like DSD - into fidelity.

Charles Smile
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sfdennis

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Re: George....what's the resolution of analog?
« Reply #37 on: May 16, 2004, 09:31:55 am »

Hey Charles, that is a very funky converter indeed. What is it exactly? At first blush, it looks like there is absolutely no reconstruction filter working. Also please let us know the time & voltage division settings are on that picture. -Dennis
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Dennis Tabuena

Chuck

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Re: George....what's the resolution of analog?
« Reply #38 on: May 16, 2004, 11:45:11 am »

sfdennis wrote on Sun, 16 May 2004 15:31

Hey Charles, that is a very funky converter indeed. What is it exactly? At first blush, it looks like there is absolutely no reconstruction filter working. Also please let us know the time & voltage division settings are on that picture. -Dennis


Hi Dennis,,

it is the output of a Burr-Brown PCM1704. I did some glue logic, and so was able to remove the DF1704 oversampling filter, that I was used to employ.

So the stair that you see, is just the exact amplitudes, stored on the CD. The stair signal unfiltered sounds not so good, as you might guess, and with RC filters, you only smooth the first edge, but not the second.

So I tried this audio-transformer and it works and sounds very good.

I like higher sampling rates, because not only more information is captured, but also with higher sampling frequencies the steps are smaller in amplitude and filtering is much easier.

One of the big advantages of higher sampling rates is that digital- or oversampling-filters (with their look-ahead and start ringing before the signal) become obsolete.

Well, in my opinion, they should not be used anymore - in other words: don't let a mathematician interpret audio signals.

I don't remember the scope settings, but at 44.1kHz each stair should be about 23
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Ethan Winer

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Re: George....what's the resolution of analog?
« Reply #39 on: May 16, 2004, 12:34:46 pm »

David,

> Yes, we have many tests (measurements) that are useful and give some indications of device behavior, but they are simply "easiest path" devices, that is, measurements we CAN make but not really all the measurements we would WANT to make. <

Everything important in audio that needs to be measured can be measured using currently available tools. These measurements can resolve to a level much finer/lower than anyone's ear can hear. There are no magical properties that we can hear, but which science has not yet identified. If you believe otherwise, I'd love to see some evidence.

--Ethan

Ethan Winer

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Re: George....what's the resolution of analog?
« Reply #40 on: May 16, 2004, 12:41:43 pm »

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.

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.

--Ethan

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Re: George....what's the resolution of analog?
« Reply #41 on: May 16, 2004, 12:49:59 pm »

Chris,

> You can measure truncation artifacts. You can measure jitter. <

You can measure noise, distortion, and timing errors like jitter on a Studer too. The jitter caused by tape scrape on even the best analog tape recorder is 100 times worse than the jitter of an SB Live sound card.

> there is no scientific basis for behaving like a Sound Blaster beats a Studer. <

And there is no scientific basis for behaving like a Studer beats a SoundBlaster. If you believe you know of such a basis, I'd love to hear it.

> the tape machine head bump the Studer would have is significant in frequency response terms, but extremely unobjectionable. <

Okay, you may well enjoy hearing a slight bass boost at a pleasant frequency. So why not just add that with EQ? How can you argue with a straight face that an obvious flaw like a skewed frequency response is a feature or not objectionable?

> What about the on-the-fly SRC built into some Sound Blaster Audigys? These things can be both measurable, and acutely unpleasant. <

A proper double-blind test will put that to bed quickly.

--Ethan

dwoz

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Re: George....what's the resolution of analog?
« Reply #42 on: May 16, 2004, 01:35:41 pm »



Let me give a shot at it...what the hey, eH?


Ok, "resolution".

when an analog signal is sampled, it is essentially 'sliced' into segments, each of which has a certain width in time. The width of the 'slice' is dependent on how many slices you make in a second...the sample rate.

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.

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.

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.

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

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.


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

But, being able to calculate the slope of the signal, lets me "find" a lot more information about that analog signal than is immediately apparent in the raw data.

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

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.

As a little social aside...so good to have curveDominant around to save us newbies from ourselves.

Reread Zoesch's comments...

dwoz
david wozmak
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Bill Mueller

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Re: George....what's the resolution of analog?
« Reply #43 on: May 16, 2004, 01:48:35 pm »

Wow,

This thread is all over the place. I am most comfortable with Phill Graham's response however I would like to add a couple of things.

First lets define "analog". Are we speaking of analog electronics or storage?

In analog electronics, functional resolution (detail) is determined by high frequency bandwidth. If high frequencies come in but do not go out of a circuit, the resolution is reduced. Noise and distortion both limit resolution by introducing signal components not found in the source.

In order to create an "analog" (aproximate representation) of an acoustical event, there needs to be a series of conversions of energy (transductance), by a series of transducers, each with unique resolution limiting parameters.

The first transducer stage is mechanical. The diaphram of your microphone moves in approximate syncronicity with compression and rarefaction states of molecular movement in the air. The resolution limiting factor here is mass. The heavier the diaphram, the slower its response and the more bandwidth limiting is its perfomance.

The second stage is either magnetic or electrical. Ribbon and dynamic mics transduce mechanical motion into magnetic energy and condenser mics convert that motion directly into electrical energy. Phil's description regarding magnetic transfer applies wherever transformers are used. Nonlinear transfer due to the hysteresis curve adds both noise and distortion, both resolution limiting factors.

Once into the electronic stage, there are any number of limiting factors regarding high frequency response however, my view has always been that noise is a major mitigating factor regarding high frequency performance. Since noise is associated with all frequencies in a circuit, making a circuit's high frequency performance wider than necessary, will introduce noise unnecessarily. Building a circuit both wide and quiet is the trick. I won't go any further here because the best of the best can give their views on how they accomplish this.

With analog STORAGE high frequency performance is limited by the speed of the individual magnetic domains on the tape as they go by the record/play heads. There are two ways of increasing high frequency performance. First you can move the domains by the head at a faster pace thereby spreading the high frequency signals over more physical domains. This is why a 30ips Studer A-80 MkIII can record 30khz and your analog cassette machine is limited to about 12khz. The other way is to reduce the individual size of the domains. The problem here is to maintain sufficient "retention" in the domains so that they will not loose their magnetic energy. Larger domains naturally have better retention. Better retention means better signal to noise specs.

Again, the magnetic hysteresis curve defines the linear transfer capability of a magnetic medium. We use biasing to linearize magnetic tape, but at the cost of adding noise. Designing the best compromize between noise, distortion and bandwidth is the art.

I see the domain size/speed issue as being the analog storage analogy (sorry) to sample rate in a digital system. The higher the sample rate (analog tape speed) the better the high frequency performance.

As regards to the sine/square wave storage issue. Anyone who believes that we store perfect waveforms on an analog recorder better take a closer look at a 20khz sine wave at +4 on almost any analog recorder output.

One last pet peeve. It is necessary to have ALL test parameters available to believe ANY stated performance specs and ANY piece of gear, analog or digital.

Best regards,

Bill

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George Massenburg

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Re: George....what's the resolution of analog?
« Reply #44 on: May 16, 2004, 01:58:07 pm »

gtphill wrote on Sat, 15 May 2004 21:20


[...]
Let's start by trying to define "resolution."  A common definition for this in physics is the Ralyeigh limit for optical "resolution."  It is approximately equal to .66*lambda.  It says that two objects closer together than .66*wavelength cannot be focused on well enough to tell one from the other.

In some sense the Nyquist frequency can be thought of as the limit of the (frequency,wavelength,length-however you want to look at it) "resolution" of a discrete time system.  Below the nyquist frequency all waveform content is completely captured, and above the nyquist frequency it aliases back into the lower frequencies (an erronius result).
[...]
I am tempted to talk about other subjects, such as electron thermalization, johnson noise, etc. but I don't want to devote further time to this before I see if it is heading in the direction you were looking to comprehend.

Phil,

Thanks very much for your notes.  Now, this is alot closer to the discussion that I think  we should be having about digital audio.  I'm currently having a enlightening discussion off-line with Jim Johnston about quantizing multi-channel audio and differential resolution in the time-domain.

To those of you who are dreaming of perfect waveforms, I have to reiterate what others in these two threads are saying very clearly, "You're barking up the wrong tree."  IT'S NOT BANDWIDTH.  I, like others, wish you guys would first just do the reading leaving your at-best-unproductive prejudices behind.

Perhaps what we should do is to start a thread where we do not allow any of the "magic thinking" stuff.

Stay tuned.

George
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