How can digital be more spectrum efficient than analog ?

Lets define "Bandwidth"- Bandwidth properly refers to spectrum & is measured in Hz. If you're talking "bitrates" then you're refering to a system with a fixed transmission capacity. Whether or not it's being used efficiently is measured by what % of the data stream consists of overhead messages & empty data octets.

The OP was talking about "efficiency", more or less relating to voice circuits. Without a doubt the standard reference of a 4 KHz voice channel it's more efficient spectrally to use FDM than to move 24 voice channels than to use a T1. In fact, as the T1 spec requires a pulse shape that's more or less square that implies at least 3rd order harmonics @ 4.5 MHz. You can fit 600 FDM voice channels in that space.

Well, that sort of figures as a standard digital voice channel is

64K/sec anyhow. You certainly can't squeeze a higher bitrate from your modem through there. & how much you can send depends on the card, if its using robbed bit signalling (yes, its still in use here & there) you're limited to 56K. If you have a crappy phone line with poor S/N your rates going way down. A pointless quibble perhaps but its late & I'm bored.

From the OP's question I'd say you're putting the cart before the horse. Bitrate uses Bandwidth, spectrally speaking. How much depends on the modulation method, QAM, QPSK, FSK, FM, CW yadda yadda. Bandwidth is not an unlimited resource, not everybody has the luxury of multiple dark fibers in the ground between here & there. There are very real- er, um, real world constraints with systems such as satellite, terrestrial M/W & the previously mentioned wireless systems.

I could have sworn thats what I was getting at by way of the examples of cellular transmission standards, but what the hell do I know ???

Agreed. Whole heartedly.

Unfortunately bandwidth is never unlimited & the noise level can occaisionally be out of your control. Digital systems are far less tolerent of noise when it *does* exceed the critical level. Analog systems get "hissy", digitas ge& ..or_de^5T3+...

True, although as I also alluded to encoding & error protection schemes eat into the actual traffic throughput for a given system at layer 1. You can over come a shit load of noise with the right setup, but if you have to send a million bits to get one bit of payload through to the customer you're better off hand delivering the message.

H.

Duly ignored, Jerry. :=)

The antenna's noise power scales directly with the

Caveat: Only if the FET impedance is very high compared with the source impedance. This would imply an operating frequency well below VHF.

If the receiver has 0 dB noise figure, SNR is

Hence comparing bandwith (spectrum) to bitrate (capacity) is nonsense. Added prattle doesn't change that.

T1 does *not* require a square pulse shape. It requires 750 Khz bandwidth. It was not designed for efficient spectrum utilization, because that is not required on a twisted pair cable. However, since it was designed to replace a single 4 KHz voice circuit with 24 each

4 KHz voice circuits (granted with lower SNR), it is hard to accept your argument that a T1 represents bandwidth inefficency as such.

Since nobody puts 600 FDM voice channels on a twisted pair, I can't see where you can claim that many will fit, eh?

Line cards know nothing about robbed bit signaling. And therefore robbed bit signaling has nothing to do with the bit rate for a PAM digital signal on the wire side of a line card.

Which is why bandwidth *provides* more bitrate. You are confused.

So?

Swear all you like, but that isn't what you said.

A useless statement of no significance.

Wrong. A digital system can function error free at an SNR so low that analog systems cannot function at all, much less simply get hissy.

More prattle?

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com

Thanks, that was OK, but little new to me.

IMO TDM can't carry more [nor less] info in the same bandwidth than FDM. The apparent 'gain' is acheived by rejecting the redundancy. There's nothing for nothing, and 'calling it compression' hides the reality of 'rejecting the redundancy'.

No, "Less fidelity" doesn't count as 'specrtum efficiency' ! Think/understand 'conservation of matter, energy, momentum ...etc'.

== Chris Glur.

Nuts from the point of view of maximizing power transfer. Not necessarily nuts from the point of view of eliminating resonances and reflections in the transmission line.

...

It's clear to me that reducing the fidelity of a signal can save transmission resources (bandwidth, time, energy). Do you disagree? Sending a signal using smaller bandwidth without degrading it: is that what you mean by "spectrum efficiency? If so, where does it fit in the discussion.

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Agreed (and mentioned in passing at some point). But I don't think that Randy had reflection in mind when he asked the question I responded to.

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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...

I think you simply missed the significance.

A digital system useful where SNR is very low has a very low threshold and very low throughput. A system intended for a clean channel behaves as H.E. described it. You guys seem to be describing different parts of the elephant.

...

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Non-sequitur, but what you really meant to say is also wrong! You just stepped-on Shannon yourself. Where the rubber meets the road, there is no "digital system." Everything is analog. (In a digital environment there is no noise, so SNR is a useless concept.)

While Shannon measures information in "bits", he is not talking about communicating in a digital environment. Analog channels pass information bits subject to the SNR vs. Bandwidth trade-off formally expressed by Shannon.

Indeed, "a digital system can function error-free at an SNR so low that analog systems cannot function at all..." but that is entirely irrelevant. To achieve this magical feat, it must do so at a reduced *information* rate (forward-error-correction bits, retransmissions, etc. don't count as information).

It depends on how much of the "big picture" you want to include. It seems intuitively reasonable that reducing the fidelity of a signal increases the probabilty that the message will be useless at the receiving end (and will have to be retransmitted). Because of this, it seems likely that reducing the fidelity will increase channel efficiency to a point, after which it may actually degrade it.

I'm not sure how to reconcile "no-top-post's" remarks about "conservation of matter ..." with this observation, however.

It is a non sequitur, with no significance to the statement it references. Nobody has suggested there is such a thing as unlimited bandwidth, ever. That was not part of the discussion, and adds nothing to our understanding of why or when a digital system is better or worse than an analog system. It certainly has nothing to do with the quoted statement retained above regarding the SNR threshold characteristic of digital carrier systems vs. the additive noise of analog systems.

Fiber optics is a well understood example of a low SNR environment where digital carrier systems provide significant advantages in an environment where analog carrier can barely function. Clearly fiber is not a system with very low throughput...

It may be true that a system intended for a clean channel behaves as he described, but that does not negated the fact that a system which must operate under less than optimum conditions does *not* work as he described.

--
Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com

You are thoroughly confusing the terms "analog" and "digital" with specific types of modulation methods. Later on in this post, you seemed to suggest that analog (in a fiber channel) must somehow be equated to baseband signalling.

H.E.'s observation is not a non-sequitur. It is, in fact, central to the concept of a trade-off between noise and bandwidth. Anyone who understands Shannon also understands that you, yourself, "suggested that there is such a thing as unlimited bandwidth", when you stated that "above a minimum SNR, digital systems are essentially error free": "error-free" with non-zero noise and an information rate greater than zero implies infinite bandwidth. That is, unless you were actually talking about a digital system (where there is no noise) rather than a modulation technique, in which case, you are the one spewing non-sequiturs.

That paragraph is erroneous on each and every point. You obviously do not understand what defines a "digital" system.

And you should read Shannon's paper...

The first two parts to Shannon's 1948 paper titled "A Mathematical Theory of Communications" are labeled "DISCRETE NOISELESS SYSTEMS" and "THE DISCRETE CHANNEL WITH NOISE". Those are an analysis of digital systems, first without noise and then with noise. Part 4 is titled "THE CONTINUOUS CHANNEL" and Part

5 is "THE RATE FOR A CONTINUOUS SOURCE", both of which are analysis of analog systems.

Apparently not to the telephone industry! They have long since been taking advantage of that to make fiber optic systems ubiquitous.

(I might note that it was not irrelevant to Claude Shannon in the 1940's either... the first sentence in his 1948 paper says, "The recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication.")

"forward-error-correction bits"???

Whatever. Do you know what the SNR on a typical fiber optic cable is, and what the typical bit error rate for fiber digital systems is?

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com

Presumably, a deliberate sending-side fidelity reduction doesn't render a message useless. If it did, there'd be no reason to send it. One can, for instance, send readable text with six bits per character by using only upper case (or only lower case, as some esteemed posters do anyway).

It takes a lot of fidelity loss in the channel or the receiver to render some signals useless. Considering the limited fidelity of some car radios (or that my hearing doesn't extend to the top two notes on a piano) much of the broadcast fidelity is lost on me. A narrower channel might just as well have been used.

It's too oblique for me also.

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

I think you may interpret the statement too literally. To me, is a statement that bandwidth is a limited resource, equivalent to "Bandwidth doesn't grow on trees."

All electromagnetic signals are analog. The throughput of a noisy fiber only seems high by other standards. Considering the analog bandwidth (and hence the potential throughput) fiber crawls.

Agreed.

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Yup, I'll confirm that I didn't have reflections in mind. If an analogy could be made between "power" in traditional analog systems and "information transfer rate" in digital systems, then I was referring to "power" transfer, which translates to information transfer rate.

--
%  Randy Yates                  % "Ticket to the moon, flight leaves here today 
%% Fuquay-Varina, NC            %  from Satellite 2"
%%% 919-577-9882                % 'Ticket To The Moon' 
%%%%            % *Time*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

To push the analogy further, information would be like joules and information rate would be joules/second = power.

--
%  Randy Yates                  % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC            %  sliding, it's magic."
%%% 919-577-9882                %  
%%%%            % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Hokey, dokey! You have the right to remain ignorant...

This is an interesting side trip. What, exactly, are we talking about when we use the term "fidelity" in an information-theoretic sense? Shannons studies have shown, (and are frequently quoted in sci.crypt--where they are important for another reason) that English text has between

1 and 5 bits of information per character, so six bits per character represents a certain amount of redundancy. Does "fidelity" of the channel mean we reproduce all the redundancy correctly? How much "fidelity" do we need to send Mozart from one end of a channel to another "correctly"?

With regard to your point about a deliberate sending-side fidelity reduction, etc.: I don't think that deals with the fact that the fidelity of the sending-side cascaded to a channel is seldom under the complete cognizance of the sending side. Consequently, without having some additional information, one cannot determine a-priori whether the fidelity of the sending side (ahead of the channel) is good enough.