"what you're bringing out is that Shannon's capacity theorem,
C = W*log_2(SNR+1)
depends on bandwidth (W) *and* SNR, while analog transmission usually only considers bandwidth."
Here's a hint: that is nonsense. Do you expect posting that sort of statement is supposed to go without comment just because the poster is an old hat in one of the several newsgroups this is posted to?
My apologies. I read what you said instead of what you meant. You did not specify anything other than the capacity of the analog system. If you had specified "maximum capacity" or "Shannon's capacity" or in some other way indicated what you actually did mean, I would have answered that. You didn't.
Nice whine, but it does not refute the above criticism of what was said. You are obfuscating exactly which "channel" is under discussion. Th original discussion was about the "digital communications channel" provided by the modem as a whole, which includes one or more distinct digital channels provided internally by the modem (which typically use an analog channel provided external to the modem). They are not the same channels, and you cannot discuss them without making a distinction about which you mean.
"depends on bandwidth (W) *and* SNR, while analog transmission usually only considers bandwidth."
Did he actually say that? Is it true that the *entire* post I was responding to was nothing other than similar statements?
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Floyd L. Davidson
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com
"Isolation" has nothing at all to do with whether a signal is or is not baseband.
DS1 and DS1E (T1/E1) are definitely baseband signals. If you study their signals you will see they readily pass through their appropriate transformers.
I had a BASIC version of Eliza on my Amiga a couple of decades ago...you could forward the output to the voice synthesizer and have a conversation with it (well, I had to type, anyway)...
Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions.
If you think there's something wrong with the statement why don't you explain what's wrong and why you think so? Just nay-saying and then denegrating others makes you look like the worst of the trolls that show up here from time to time.
Randy did clarify in response to your post and conceded that there's nothing inherently digital in Shannon' capacity formula, so I don't know why you keep hammering on that.
What he said, as quoted above, was:
"I can't think of an analog system that uses an analog modulation scheme that takes advantage of both SNR and bandwidth to reach "capacity." Can you name such a scheme?"
What's the problem? He asked if you knew of an analog modulation scheme that reaches capacity. Capacity is a well-defined concept and since you brought Shannon's paper into the discussion you should understand what "capacity" and "reaches capacity" means. There's no ambiguity in the statement, but the fact that it takes you a couple of posts of dancing around it just seems to be further indicative that you don't understand this stuff.
So how about you define the channel and what you think "capacity" is in that channel and then we'll go from there. FWIW, in the context of Shannon's paper the "channel" impairment is just AWGN. It's only been the last decade or so, really the last several years, where people have been really actively discussing capacity in the context of multipath channels, usually in the context of MIMO schemes. Research has been going on for much longer than that, but working with capacity computations for other than AWGN has only really hit the mainstream recently in my experience. But for satellite systems, which you're more familiar with, the channel is generally AWGN plus a little distortion from the transponder and the rf electronics. For the most part unless you're on the edge of the transponder bandwidth or using a really crappy rf system, AWGN is a fine channel model for satellite communications. So, just to make life really easy on you and make the discussion simpler, I'm quite happy to assume (which I have been, anyway), that we're talking about AWGN channels, just like in Shannon's paper.
FWIW, that's really independent of whether the scheme is analog or digital, too, so that should make you happy.
If that's not a distinct enough definition for you then please feel free to suggest modifications, but justify them with a rationale.
Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions.
Something I've griped about before, so please forgive me for climbing on this particular soapbox yet again...
Digital does not precisely equate to "discontinuous," any more than analog precisely equates to "continuous" (even though the common implementations of both sorts of systems most definitely adhere to this distinction). The terms really refer solely to two means of expressing or encoding information; given that interpretation, nature itself is neither "analog" nor "digital" - nature simply IS. It is the description of nature that can be presented in analog or digital form.
Of course, the moment your micrometer touches the bar, you've changed the library. Depending on just which volumes are lost, that may actually be an improvement....:-)
If I might interject just a little here - with all due respect to both sides....
After looking through the last N posts in this thread, I have come to the conclusion that BOTH of you seem to know what you're talking about, but that you also both seem to be having some problems expressing yourself to the other - in several cases, using some terminology/phrasing that was ambiguous at least, and I think this is causing a good deal of this "you're confused/no, YOU'RE confused!" sort of exchange.
Perhaps it would be beneficial at this point for all involved to simply take a few deep breaths and consider how best to answer the original question with sufficient clarity and simplicity? If that's already been done, then what's the point in continuing?
I would have to disagree somewhat with the above definitions. The true difference between "digital" and "analog" encoding schemes is not whether the information is "discrete" or "continuous," but in how the signal is to be interpreted to recover the intended information.
In an "analog" system, simply put, some parameter of the signal (voltage, let's say) is considered as varying "analogously" with the information being conveyed (and hence the very name, "analog"). Variations in voltage represent variation in sound, for instance, in the case of an "analog" audio recording. In a "digital" system, again defining this as simply and as broadly as possible, the information is being conveyed in numeric (well, more broadly, "symbolic") form (i.e., as "digits"), and there is no clear correlation between any given signal parameter and the original information (in other words, you have to have a "cheat sheet" - whether or not it's explicit or just implied - to translate the information back into usable form.
To be sure, most "digital" systems do use discrete states, and most "analog" systems are continuous, but those are not fundamental or inherent requirements to the terms themselves. Examples of discrete-state analog information transmission aren't even all that uncommon - an analog video interface, especially one conveying information originally created in the form of discrete pixels (spatial samples of an image) is one such. If we started with discrete pixels of, say, only 3-4 bits per color each, and you are using the typical raster-scan image structure, then the only way to make sense of the signal is to treat it as a collection of discrete samples and present it as a 2-D array of such; you have to sample the analog signal at the proper times to recover the proper pixel values, and the transitions between them provide no relevant information whatsoever (excepting, of course, that you can use the transitions, and a little bit of cleverness, to figure out what the correct pixel timing should be).
One result of this perspective is that there really isn't any such thing as a "digital" or "analog" signal, fundamentally - signals (at least within the context in use here) are just electricity. The "digital/ analog" distinction lies solely in how that bit of electricity is (or was intended to be) interpreted.
I have previously quoted most of these, but repeating is not a bad idea:
formatting link
I have paired off definitions, with the exception of two that are missing the "analog" side of the pair.
(Note: They do not list a definition for "analog".)
digital: Characterized by discrete states.
analog data: Data represented by a physical quantity that is considered to be continuously variable and has a magnitude directly proportional to the data or to a suitable function of the data. (188)
digital data: 1. Data represented by discrete values or conditions, as opposed to analog data. (188) 2. Discrete representations of quantized values of variables, e.g. , the representation of numbers by digits, perhaps with special characters and the "space" character.
(Note: They do not list a definition for "analog modulation".)
digital modulation: The process of varying one or more parameters of a carrier wave as a function of two or more finite and discrete states of a signal. (188)
analog signal: 1. A signal that has a continuous nature rather than a pulsed or discrete nature. Note: Electrical or physical analogies, such as continuously varying voltages, frequencies, or phases, may be used as analog signals. (188) 2. A nominally continuous electrical signal that varies in some direct correlation with another signal impressed on a transducer. (188) Note: For example, an analog signal may vary in frequency, phase, or amplitude in response to changes in physical phenomena, such as sound, light, heat, position, or pressure.
digital signal (DS): A signal in which discrete steps are used to represent information. (188) Note 1: In a digital signal, the discrete steps may be further characterized by signal elements, such as significant conditions, significant instants, and transitions. Note 2: Digital signals contain m-ary significant conditions.
analog transmission: Transmission of a continuously varying signal as opposed to transmission of a discretely varying signal.
digital transmission system: A transmission system in which (a) all circuits carry digital signals and (b) the signals are combined into one or more serial bit streams that include all framing and supervisory signals. Note: A-D/D-A conversion, if required, is accomplished external to the system. (188)
That is not a valid definition. The variation must be continuous, i.e., it must not be discrete.
An interesting definition... but not a valid one.
Indeed, that is true because those *are* the accepted standard definitions.
Clearly they *are* inherent requirement.
Lets not argue over examples. If you use the wrong definition the example is not correct.
Again, fundamentally flawed because the wrong definitions are used.
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Floyd L. Davidson
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com
I have quoted Federal Standard 1037C definitions and have been referring directly to Shannon's paper as well as other standard engineering texts when I write, in an attempt to avoid as much ambiguity as possible. That effort of course can never be totally successful, and I do think that a good deal of the confusion is not over how it works, but over how to describe it.
That statement aside though, even *more* confusion exists over how it actually works! Even at the very basic level of defining digital and analog...
I have once again posted, in another article, several standard definitions in an attempt to prevent the "digital means..." debate from becoming too involved.
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Floyd L. Davidson
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com
Note the word "usually". The "usual" methods of what are commonly called analog modulation schemes (AM, FM, SSB, etc.) that fully use a given bandwidth channel don't allow a doubling of capacity if the noise floor drops enough. Whereas what I (and maybe the OP) call digital modulation schemes (QAM, etc.) do (stretch the constellation vertically in my example).
I didn't see much of an explanation of why you thought it was wrong, only that you did and that you thought it "nonsense". And my read of Randy's response didn't look to me like an admission of being incorrect, just a clarification and agreement that he, too, recognizes that Shannon's basic capacity formula is generic.
No problems here. And you?
BTW, maybe get around sometime to answering the questions I posed for you. If you think we're just misunderstanding each other then they may help clear it up.
Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions.
The signal on the wire passes through the transformers because it has been manipulated to *not* be at the natural baseband of the T1 bitstream.
The raw T1 bitstream has DC content. If the frames are mostly zero or mostly one, the DC component predominates. The signal is manipulated before it reaches the wire to get rid of that DC. So, the wire does
*not* carry the natural baseband of the T1 signal. This has *everything* to do with isolation. If there were no need for isolation, you could have a path that works down to DC, and the raw T1 bitstream could flow along it.
Just two comments at this point: first, a dictionary should never be used as a textbook (for that matter, no matter WHAT is in a book, if it doesn't make sense it is simply wrong, no matter who wrote or published the book). This is an example of an "argument from authority," and that's not a particularly strong form of argument. I can show you, if you like, another published text (from a reputable publisher and editor, even!) which contains exactly the definitions I gave previously. (The fact that I wrote the book in question might have something to do with that, I admit...:-)).
The second comment is that "characterized by" is a phrase which indicates that you're being given some simple guidelines for recognizing certain things as they are typically encountered in practice. That doesn't mean that the characteristics being described are necessarily central to the fundamental definition of the item in question.
This is simply wrong, or at least not a sufficient distinction. I can fairly easily point to examples of practical, real-world signals which are undeniably carrying information in "analog" form, and yet have been constrained to a limited number of finite states. With a little thought, I'll bet you can too.
For instance, let's say I show you an oscilloscope trace in which the observed signal is varying between two and only two levels at varying intervals. This is the only information you are given. I then ask you if the signal in question is:
A) Showing you a portion of a serial digital data stream,
B) Showing you a portion of an analog video signal, coming from a camera which happens to be pointed at a patern of varying-width black and white vertical lines, or
C) Can't be identified as either "analog" or "digital" from the information given.
Since there's no good way from the information given to tell if you're looking at case "A" or "B," "C" is the only possible honest answer - and therefore the definition given above is not adequate. You cannot distinguish between certain real- world "analog" and "digital" signals from this definition alone.
So by this definition, is what comes out of an AC outlet an "analog signal"? All this is required of the above is that the signal be "continuous," so this certainly would seem to qualify. But that signal carries no information whatsoever, so to speak of it as either "analog" or "digital" is meaningless.
Why use "analog" as a stand-in for the perfectly good word that we've already got to say what we really mean here: "continuous"?
Why? Simply because the definition found in one particular standard says so? What forces an "analog" representation to be continuous? (And before you answer that one, let me add that I can fairly easily point to practical, real-world examples of analog signals and/or systems which are not continuous it at least one, and in some cases several, way(s).)
Again - why not?
But so far, you have given no reasons for making that claim. To argue the equivalent of "this definition is the correct one, because the definition says so" is very clearly circular.
OK - what makes one definition correct, and another wrong? I've spent a good part of my career working in the area of standards and specifications - and as a result, I wholeheartedly belive in the old adage, "the nice thing about standards is that there are so many to choose from!" Sorry, but what's right and what's wrong is a matter to be determined through evidence and rational argument, not by the vote of a committee.
"The true difference between "digital" and "analog" encoding schemes is not whether the information is "discrete" or "continuous," but in how the signal is to be interpreted to recover the intended information."
That is your definition, and it does not match. All of the various standards organizations which contributed to FS-1037C and MIL-STD-188 are not wrong, *you**are*.
That is not a dictionary. It is a glossary of *standardized* definitions. They are not _describing_ common usage; they are _providing_ working definitions.
If you check it out, you'll find that many of them are not only FED-STD-1037C, but also are from MIL-STD-188.
Argumentum ad Verecundiam is valid if it meets three criteria. The authority must actually be an expert on the topic, virtually all such experts must agree with the opinion given, and the cited quote must be a valid expression of the expert's opinion.
As you can see, citing standardized definitions is the *only* way to prove the validity of a set of definitions.
The simple fact is, if *you* do not agree with the definitions provided, then it is *clear* that you do *not* understand the topic. There is *no* other possible option.
That would of course be a false appeal to authority. You 1)
*clearly* are not an authority, and 2) do not agree with virtually all authorities. I will assume that you do meet the third criteria and are not misquoting yourself... ;-)
That statement is absurd. Why else do you suppose they say that, and say nothing else? Of *course* they are fundamental and necessarily central to the meaning of the terms.
No, that *is* the *Standard* definition of the term. *You* are wrong. (Note the 188 footnote, which indicates it comes from the Mil-Std specification.)
The simple fact is, you cannot. By definition if there are discrete values from a finite set, it is *digital*. Anything you cite which meets that criteria is digital by definition.
The rest of your commentary is not worth responding to, as it is redundant to argue with points based on proven false premises.
--
Floyd L. Davidson
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com
That is not true. If you have any experience with FM microwave systems using FDM carrier, you'll recall that the noise floor is
*essential* to maintaining channel capacity.
Just increase the baseband loading enough, and the effects are rather easy to measure.
The statement above is *clearly* saying that digital is affected by both bandwidth and noise, while analog is not. That is not true.
But there are of course *both* digital and analog systems that do not make use of the entire range of either bandwidth or SNR in the available channel. The point is *still* that any attempt a differentiating the two in that manner is not valid.
--
Floyd L. Davidson
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com
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