[another_someone]

We all use data compression when we send files to each other. To get the maximum useful information rate across, you need to take a lot of delay in the system. This allows you  to code the information efficiently and to check and correct errors.  It's fiendishly complicated but 'they' are making advances all the time. It's why you can get such a lot of programme time on a DVD or MP3 player, these days.  Present systems still waste a lot of channel capacity because the coding is  not ideal. It gets better all the time, however.

MP3 and DVD's (they use MPEG2, do they not) do not use lossless compression, so they are not merely making more efficient use of bandwidth (in the way that Huffman or LZW encoding do), but actually throw away data - hence the Shannon limits are not totally pertinent to them (this is compounded by massive amounts of error correction that reduce the efficiency of bandwidth usage).

[lyner]

Fair enough - I quoted those well known forms of compression as the lossless compression methods are, perhaps,  not so well known.
I would disagree that error correction makes for inefficiency when you bring into the account the signal to noise consideration. You may get garbage out of a system that, with a good snr, is what you would call efficient but which is passed through a noisy channel. The way you demodulate and decode your received signal is the crucial thing in its information rate capacity.
You can cram more and more into a channel and get worse and worse inter symbol interference but, as long as the snr is high enough, you can get all the info out again. That's, basically, what Shannon says and I wouldn't lightly disagree with the Daddy.
To do the above, you need to filter over a longer and longer  time interval - which introduces a longer and longer delay into your channel and more complex processing..
Bandwidth Usage is not just a matter of raw data rate per Hz of channel space.

[neilep (OP)]

THANK EWE again for your continued wonedrful posts !!

May I ask please what a NYQUIST limit is?...and does it have anything to do with a flavoured milk drink?

[Karen W.]

Which I love!

[Alandriel]

NYQUIST limit?!?!?!

I have a friend who's last name is Nyquist (a quite commen Swedish name I believe).
Never knew she had a limit.

 []


Gosh - what an interesting thread


..... my braincells are devinitely doing backward and forward flips now.


So much to learn - so little time.......

[another_someone]

THANK EWE again for your continued wonedrful posts !!

May I ask please what a NYQUIST limit is?.

http://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem#Nyquist_rate

Nyquist rate

In 1927, Nyquist determined that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel. In symbols,



where fp is the pulse frequency (in pulses per second) and B is the bandwidth (in hertz). The quantity 2B later came to be called the Nyquist rate, and transmitting at the limiting pulse rate of 2B pulses per second as signalling at the Nyquist rate. Nyquist published his results in 1928 as part of his paper "Certain topics in Telegraph Transmission Theory."

and does it have anything to do with a flavoured milk drink?

Only insofar as Nestle is a Swiss company, as Monica is Swiss, and:

NYQUIST limit?!?!?!

I have a friend who's last name is Nyquist (a quite commen Swedish name I believe).

http://en.wikipedia.org/wiki/Harry_Nyquist

Harry Nyquist (February 7, 1889 – April 4, 1976) was an important contributor to information theory.

He was born in Nilsby, Sweden. He emigrated to the USA in 1907 and entered the University of North Dakota in 1912. He received a Ph.D. in physics at Yale University in 1917. He worked at AT&T's Department of Development and Research from 1917 to 1934, and continued when it became Bell Telephone Laboratories in that year, until his retirement in 1954.

As an engineer at Bell Laboratories, he did important work on thermal noise ("Johnson–Nyquist noise"), the stability of feedback amplifiers, telegraphy, facsimile, television, and other important communications problems. With Herbert E. Ives, he helped to develop AT&T's first facsimile machines that were made public in 1924. In 1932, he published a classical paper on stability of feedback amplifiers (H. Nyquist, "Regeneration theory", Bell System Technical Journal, vol. 11, pp. 126-147, 1932). Nyquist stability criterion can now be found in all textbooks on feedback control theory.

His early theoretical work on determining the bandwidth requirements for transmitting information, as published in "Certain factors affecting telegraph speed" (Bell System Technical Journal, 3, 324–346, 1924), laid the foundations for later advances by Claude Shannon, which led to the development of information theory.

In 1927 Nyquist determined that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel. Nyquist published his results in the paper Certain topics in Telegraph Transmission Theory (1928). This rule is essentially a dual of what is now known as the Nyquist–Shannon sampling theorem.

Nyquist received the IRE Medal of Honor in 1960 for "fundamental contributions to a quantitative understanding of thermal noise, data transmission and negative feedback." In October 1960 he was awarded the Stuart Ballantine Medal of the Franklin Institute "for his theoretical analyses and practical inventions in the field of communications systems during the past forty years including, particularly, his original work in the theories of telegraph transmission, thermal noise in electric conductors, and in the history of feedback systems." In 1969 he was awarded the National Academy of Engineering's fourth Founder's Medal "in recognition of his many fundamental contributions to engineering."

Nyquist lived in Pharr, Texas after his retirement, and died in Harlingen, Texas on April 4, 1976.

[lyner]

As I remember, the Nyquist limit relates to the sample rate needed to re-construct a signal, perfectly. The limit is two samples for the the highest rate.
In practical terms, you need to filter the signal to be sampled with a filter which lets nothing through above half the sampling rate or you will get aliasing. (Higher input frequencies than this appear as low frequency 'beat' patterns - very disturbing)
This means that you really need  a bit more than twice the highest signal frequency. Unless you are sampling a  conventional TV signal, which  (at least for stationary pictures) has a spectrum which is full of holes, in which case you can do sub-nyquist sampling and get away with it.

[Karen W.]

THANK EWE again for your continued wonedrful posts !!

May I ask please what a NYQUIST limit is?...and does it have anything to do with a flavoured milk drink?

Nyquist Frequency

http://mathworld.wolfram.com/NyquistFrequency.html
   

In order to recover all Fourier components of a periodic waveform, it is necessary to use a sampling rate nu at least twice the highest waveform frequency. The Nyquist frequency, also called the Nyquist limit, is the highest frequency that can be coded at a given sampling rate in order to be able to fully reconstruct the signal, i.e.,

[Karen W.]

Whoops, Sophiecentaur beat me. and well explained at that!

[another_someone]

As I remember, the Nyquist limit relates to the sample rate needed to re-construct a signal, perfectly. The limit is two samples for the the highest rate.

I think it works both ways - as indicated by my reply above - I believe it is both the maximum information that can be pumped through a noiseless channel, and the sample rate you need to recreate the channel (strictly speaking, one is the Nyquist rate, and the other the Nyquist frequency - neither are formally known as the Nyquist limit).

[lyner]

I think there are two separate issues here.
The sampling rate thing is more straightforward and  relates to  the initial process of sampling the original signal - say an audio programme. You can't get rid of aliasing, once you have introduced it when you need to transmit the whole of the spectrum of the source signal; it is a non-linear distortion. (TV is a special case where you can frig it a bit, due to the signal spectrum). This limit is not related to the transmission channel.
The actual capacity of a channel - which  is what you would like to maximise, when you are paying for a satellite link, for instance, relates to the total information you can get through each Hz of available bandwidth. This is very much limited by the  signal to noise ratio. You can instantly do better than a binary modulation system by increasing the number of levels used but it is clear that noise will start to impinge sooner. There is no real difference between using a multilevel system or using a bandwidth restricting filter in your channel. Inter symbol interference due to narrowing the bandwidth can be coped with by using appropriate temporal filtering at the receive end as long as the  channel noise level is low enough
If your demodulation / decoding system is clever enough, you can squeeze a fantastic amount through. Error handling is necessary - to deal with the occasional spike, in all types of noise, but the overhead used for it is offset by the overall increase in  useful capacity.
Systems get more and more complex, of course, and the problem of standardisation  rears its head.
Wikkers has this to say about it.
http://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem#Comparison_of_Shannon.27s_capacity_to_Hartley.27s_law
and here's an article about how well they are doing these days.
http://www.sciencenews.org/articles/20051105/bob8.asp

The original question was about a fibre optic system and the full answer must involve the effect of noise.

[lyner]

Karen W
I like your  technical stuff but I have a problem with  your picture of Nestle products. They (Nestle) are playing hell with the third world health by marketing formula milk where it is  not safe to use because the available water is poor quality - they are 'dissing' breastfeeding in an area where it provides a useful barrier against disease for small babies.
Not relevant to Nyquist but I thought I'd get it off my chest. Is this too political?

[another_someone]

Karen W
I like your  technical stuff but I have a problem with  your picture of Nestle products. They (Nestle) are playing hell with the third world health by marketing formula milk where it is  not safe to use because the available water is poor quality - they are 'dissing' breastfeeding in an area where it provides a useful barrier against disease for small babies.
Not relevant to Nyquist but I thought I'd get it off my chest. Is this too political?

Firstly, the picture was Neil's, not Karen's (Karen merely quoted Neil's post).

Secondly, this is going to go way off tangent, but the issue about Nestle is old news - very old (30 years old, to be exact), and rather over hyped even then.  At present, the most recent claim against them (1999, I think) was that they supplied cheap powdered milk to maternity hospitals - this argument seems to treat third world maternity hospitals as if they were children, unable to make their own judgements as to how to use material that is provided cheap or free of charge.  This really is in a different league to Microsoft supplying schools with cheap or free software, since schools would anyway use software, it may simply be a different brand - and certainly hospitals will use powdered milk, so there is nothing wrong with supplying them with such, but one has to rely on hospitals to use it sensibly and not overuse it just because it is cheap.  If you cannot rely on a hospital to use that kind of judgement, I would be very worried about how hospitals are likely to be dispensing far more dangerous things, like drugs.

[another_someone]

The actual capacity of a channel - which  is what you would like to maximise, when you are paying for a satellite link, for instance, relates to the total information you can get through each Hz of available bandwidth. This is very much limited by the  signal to noise ratio.

This is the Shannon capacity, which I don't dispute at all anything about what you say.

But the Shannon capacity is, as you say, dependent upon the noise in the channel, and not a physical limit to the channel itself (i.e. new technical innovations can always be used to further reduce noise, but no amount of technical innovation can overcome the Nyquist rate limit - since that is a limit based on the carrier signal selected).  The Shannon capacity will always be less than the Nyquist rate because even if you reduce noise to zero (clearly impossible, but at least asymptotically possible), it will still remain limited by the Nyquist limit for the given bandwidth.

[lyner]

I have to disagree with you on what is implied by the 'Nyquist rate'. There is no reference to the number of levels in the samples to which Nyquist refers. It certainly doesn't only restrict things to two levels. You can have as many levels as you like for your samples - they can, of course, even be analogue samples. Nyquist just says that you need > = two samples per second per Hz of the highest frequency in the baseband signal. That is all. There is unlimited information, possible in each sample, if you have no noise to deal with.
The Shannon capacity relates to the total amount of information what can be carried. The actual  information in each of the samples depends upon the accuracy / quantisation  / number of bits per sample. So the  information capacity is, potentially, much greater than half the Nyquist sampling rate.


This is a favorite 'Channel Capacity' equation which relates the rate above the Nyquist rate that symbols can be sent. (Looking at the problem in the way another someone stated it in an earlier post.)
Where R is the Symbol rate
B_wis the Nyquist Bandwidth -Samples per second
C is the carrier power
N is the noise power (in the receiver bandwidth)
The symbol rate (Shannon limit) can be arbitrarily higher than the Nyquist frequency as long as your  received noise level is low enough.
It is easy to send signals at nearly the Nyquist - defined limit.  Most digital systems do just that, by design. Not many systems approach the Shannon limit.
There are systems. now, which get nearly there - space comms systems, for example.


 

[another_someone]

I have to disagree with you on what is implied by the 'Nyquist rate'. There is no reference to the number of levels in the samples to which Nyquist refers. It certainly doesn't only restrict things to two levels. You can have as many levels as you like for your samples - they can, of course, even be analogue samples. Nyquist just says that you need > = two samples per second per Hz of the highest frequency in the baseband signal. That is all.

I accept your point about the number of levels, but this does not make for infinite numbers of signals, because any modulation of the carrier will create sidebands, and you will have limits to the sidebands (although it is clear that Nyquist does not seem to imply any limit on the sidebands - maybe he has assumed that sidebands reach from zero up to the carrier frequency - which clearly in not the case ever in reality, but maybe the extreme he has assumed).  Ofcourse, the closer you get to zero Hz, the less information the sideband can carry, so in the end, most of the information will be carried in the sidebands closer to the carrier frequency.

I have to admit that I don't know the maths well enough to know whether or not Nyquist takes account of the sideband limits.

[lyner]

Another  someone:

but this does not make for infinite numbers of signals

In the end, we are just talking about the total quantity of information;  whether it's a single, high definition signal of a lot of low definition signals.  Each significant bit of each sample is quite independent of the other bits (well, at least, if you don't restrict your source signal in any way) so we're talking about the total number of bits (for instance) per second of source information.

because any modulation of the carrier will create sidebands,

Yes, of course. If your modulation system gives you a flat spectrum it doesn't really matter where the notional carrier sits - because an efficient system doesn't 'waste energy' by transmitting at the carrier frequency - that is information which doesn't need to be transmitted. The information is carried over the whole spectrum of the transmitted signal.
Nyquist isn't concerned with sidebands when you're sampling, really; that is a concern in the modulation / transmission. Nor is it concerned with noise.
If you take samples (of zero duration) of a baseband signal, you end up with an infinite number of harmonics of the sampling frequency, each of which has sidebands (upper and lower) which mimic the baseband spectrum. It is, effectively, a modulation process. The fact that the lower sidebands obout the sample frequency can overlap the baseband spectrum is what can give aliases, which imposes the Nyquist limit on sample rate. For 'boxcar' samples, the spectrum is not flat.
To get things right and to eliminate the problem, your low pass filter (pre sampling) is given a cutoff frequency of F_N/2 and the rolloff, to this is made symmetrical about the -3dB value. This cancels the distortions. Group delay needs to be minimised. There are practicalities in realising this filter, which  limits the baseband bandwidth.
All this is before we quantise anything - so, as I said before, there is unlilimited information in each sample at this stage.  This is because the more sig figs in the measurement, the more actual info there is. 
Once you quantise the signal, you start to limit the information content needed for transmission.
Shannon then starts to come into it. The amount of detail you can transmit is then limited by the symbol rate, and the signal to noise ratio in the available  system bandwidth.  This bandwidth  defining filter is 'shared' between transmitter and receiver, in order to minimise / optimise  transmitter power and adjacent channel interference, when it is relevant.
If it is not relevant then the receiver filter defines the system (noise) bandwidth. I think this must be why space comms do so well, because they can afford to put all their filtering in the receiver.
Your comment about sidebands really relates to this filtering and where it is introduced.
Remember, the information carried isn't affected by the actual frequency of each sideband - each Hz of bandwidth, wherever it lies, can carry 1Hz 's worth of info.  We may think logarithmically about frequency scales but a Hz is a Hz.
The spectrum occupied by an ideal system would, I suppose extend from zero to the carrier frequency and up to twice this. But things don't have to be symmetrical. AC coupling  is bound to impose a lower limit to the rf spectrum -, in any case,  not to mention the limit due to interference!

[michaeliang]

Optical fiber can be used as a medium for telecommunication and networking because it is flexible and can be bundled as cables. It is especially advantageous for long-distance communications, because light propagates through the fiber with little attenuation compared to electrical cables. This allows long distances to be spanned with few repeaters. Additionally, the light signals propagating in the fiber can be modulated at rates as high as 40 Gb/s [2], and each fiber can carry many independent channels, each by a different wavelength of light (wavelength-division multiplexing). Over short distances, such as networking within a building, fiber saves space in cable ducts because a single fiber can carry much more data than a single electrical cable. Fiber is also immune to electrical interference, which prevents cross-talk between signals in different cables and pickup of environmental noise. Also, wiretapping is more difficult compared to electrical connections, and there are concentric dual core fibers that are said to be tap-proof. Because they are non-electrical, fiber cables can bridge very high electrical potential differences and can be used in environments where explosive fumes are present, without danger of ignition.

[lyner]

Additionally, the light signals propagating in the fiber can be modulated at rates as high as 40 Gb/s , and each fiber can carry many independent channels,

Yes they are already used to carry a lot of data. The question was / is , what sort of fundamental limit is there? You can be sure that it's possible to do a lot better than is presently achieved.

[Pumblechook]

We were told on a visit to this place but I forget what was said now. 

http://www.porthcurno.org.uk/

Info here..

http://www.emtelle.com/?id=149