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
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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.