multiplexing, channel etc.

[steveB]

What you are saying seems very confusing, and I don't follow it. I do think you are making a simple definition overly complicated. I don't feel that definition is particularly good either, but I wouldn't worry too much about it.

Basically, they are saying that a radio channel is one channel in a band of many channels. The air, is a multiplexed medium (frequency multiplexed), which many channels, including AM channels, FM channels, TV channels etc.

In the case of a wire (or optical fiber) you might have one channel dedicated to that medium.

Also, you are incorrect that a radio channel can't be multiplexed, because you can multiplex channels within a channel. If the channel is digital, then time division multiplexing can be used. Here in the USA, digital TV channels have secondary audio channels (for other languages) built into the data (SAP). There is also captions available, and additional information is encoded as well. One can even put 2 or more complete video channels into the data with higher compression ratios.

Even the old analog TV channels encoded additional information. The color information was added later, but black and white TV could still be watched. Also, the audio is at a frequency offset from the video information, so this is really two channels put into one channel.

The bottom line is that reality is alway more complicated that our classifications and terminology would indicate. Thats why I say, don't worry to much about definitions. Definitions and terminology give you a black and white view of the facts. Reality is shades of grey and colors, which should appeal to a painter guy.

 

[ericgibbs]

hi PG,

Read thru the first paragraph of this link.

https://en.wikipedia.org/wiki/Multiplexing

E.

 

[steveB]

Wow, see PG, we all have much too learn. ericgibbs reference talks about "Orbital angular momentum multiplexing", which I never heard of before. Now I have to go find out what the heck this is. It seems we can paint with more colors and shades of grey than the eye can see.

 

[PG1995]

Thank you, Steve, Eric.

I will try to summarize this discussion about the definition of a channel before ending it.

Basically, they are saying that a radio channel is one channel in a band of many channels. The air, is a multiplexed medium (frequency multiplexed), which many channels, including AM channels, FM channels, TV channels etc.

I agree with almost everything. The point of contention was the phrase "such as a radio channel". Strictly speaking, air is not really a multiplexed medium in case of radio stations, at least those ones from old days. Because when different signals are frequency multiplexed you get a single composite signal like this. In case of radio stations, no single composite signal is generated. If you don't agree with this point then I'm happy to debate it with you in order to learn more from you. On the other hand, if things are not taken too seriously then we can say air is multiplexed! Thanks a lot.

Regards
PG

 

[steveB]

PG,

The main point is that there are so many different ways to multiplex. You showed one way to frequency multiplex by taking many combined channels and then modulating the combined signals with a carrier. But nobody said you have to do it that way. If you individually modulate separate signals on separate carriers and then add them all up in the medium, that is still frequency division multiplexing. Either way, if you do it right, you end up with the various channels at separate frequencies.

The term "one signal" does not have a precise meaning. Adding by superposition is a valid way to combine. Whether you view this as one signal, or not, is a viewpoint, not a fact. If you capture that signal with a broadband antenna, then it will look like one signal, but you can identify that there are separate information channels if you look carefully. Then you will view this as many combined signals.

Again, no one is saying the terminology and definitions you have been given are perfect, or necessarily even good. But, I recommend worrying about the actual implementations and not the wording of definitions.

 

[nsaspook]

Wow, see PG, we all have much too learn. ericgibbs reference talks about "Orbital angular momentum multiplexing", which I never heard of before. Now I have to go find out what the heck this is. It seems we can paint with more colors and shades of grey than the eye can see.

I've had this discussion before elsewhere here. https://www.electro-tech-online.com/threads/a-new-twist-on-rf.125752/#post1042569
IMO and others OAM is not a new method of far-field radio modulation but is in fact a form of MIMO. This doesn't mean it's not very useful as a possible method for fiber-optic lines.

 

[steveB]

nsaspook,

Thank you for the interesting information. I have to say making sense of this is not so easy, but I think you are right that MIMO encompasses OAM. Basically, it seems to me that these techniques are exploiting the multiplicity of EM spatial modes. In principle, spatial modes are orthogonal and hence should be capable of providing independent communications channels.

MIMO in air? - That seems to have real practical potential.

However, I can see many practicality issues in doing this on fiber optic lines. It seems standard single mode fiber inherently won't support more than one guided mode (two if you count polarization states), and multimode fibers would have too many mode coupling problems. I expect highly specialized fiber designs will be needed to make this work.

Decades ago, there was a big push to implement coherent communications with light in optical fiber, but the cost and complexity didn't allow it to pan out. Standard wavelength division multiplexing with high bit rate channels and direct optical amplification methods get most of what you want at a fraction of the cost.

Then there was another push to develop lower loss optical fiber, but the optical amplification technology won out over that idea because silica glass is abundant, and literally "dirt-cheap", while exotic glasses are not.

For OAM in fibers, one needs to compare the complexity/cost of making it all work in one fiber, versus just running additional (125 μm diameter) optical fibers in the same cable, and then even multiple cables if needed.

 

[nsaspook]

The cost vs the technical ability sometimes depends on the value of the data. Long ago we used several methods of modulation in Interesting Devices (bugs) that today are being "discovered" again as general technology advances.

https://www.electro-tech-online.com/custompdfs/2013/08/comm153-liu.pdf
https://www.spybusters.com/Great_Seal_Bug.html

 

[PG1995]

Hi

I believe at this point I need to understand the concept of negative frequencies, at least to some degree if not completely. Over the last few days we have discussed the idea superficially without really getting into it.

We come across negative frequencies when dealing with Fourier series or transform. Let's focus on Fourier series case here. There are two versions of Fourier series: trigonometric and exponential. The trigonometric version doesn't involve negative frequencies; it deals with plain, straightforward, no-nonsense positive frequencies. But it's exponential form of the series where negative frequencies come into play.

I was under the impression that I had understood the concept of negative frequencies and this belief was based on the fact that negative frequencies are just mathematical constructs used to make math right. But now I believe I was wrong because my previous understanding of negative frequencies gets into trouble when dealing with topics such as modulation.

Why don't we get different result for required bandwidth when using trigonometric form of Fourier series because lower sideband is an outcome of negative frequencies and the trigonometric form has got no negative frequencies?

Further, the AC line is labelled 60 Hz and it means 60 cycles per second. If we visualize electrons movement then we can say electrons back and forth movements constitute cycles. Further, we can mathematize this movement of electrons with a phasor rotating with frequency of 60 Hz. At least, I can, in a loose sense, say that this is a 'real' phasor. But I can't say, even in loosest sense, that there is another phasor having a negative frequency because one phasor is more than enough to mathematize electrons movement!

It would be extremely kind of you if you could get help to get hold of this weird concept. Thank you.

Regards
PG


Helpful links:
1: https://imageshack.com/scaled/large/5/m5qg.jpg
2: https://imageshack.com/scaled/large/198/26cb.jpg
3: https://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/funcan2.gif
4: **broken link removed**
5: https://www.electro-tech-online.com/attachments/cs_rotating_phasor-jpg.75260/
6: **broken link removed**

 

[steveB]

Why don't we get different result for required bandwidth when using trigonometric form of Fourier series because lower sideband is an outcome of negative frequencies and the trigonometric form has got no negative frequencies?

Go back to the last post in this thread https://www.electro-tech-online.com/threads/bandwidth-etc.135665/ where you said you would work through the math we recommended. I have to conclude that you did not do this, or if you did, then you forgot the important result you got. You will never come to grips with these concepts unless you put the work in and also remember the results of the work after you do it.

So, in that thread I showed a multiplication modulation that cancelled the carrier but showed the upper and lower sideband. Then we recommended you do the more realistic case which would show the carrier and the upper and lower sidebands. Why would you just assume and draw a picture that shows the trig case giving only the upper sideband? Was this just a fantasy you made up in your head, or did you apply some math and make a mistake?

Further, the AC line is labelled 60 Hz and it means 60 cycles per second. If we visualize electrons movement then we can say electrons back and forth movements constitute cycles. Further, we can mathematize this movement of electrons with a phasor rotating with frequency of 60 Hz. At least, I can, in a loose sense, say that this is a 'real' phasor. But I can't say, even in loosest sense, that there is another phasor having a negative frequency because one phasor is more than enough to mathematize electrons movement!

With phasors, the time variation exp(jwt) is assumed and left out of all of the math. This is assuming a positive rotation or positive frequency. You would get the same logic and usefulness if you did phasors assuming exp(-jwt) time dependence.

As I mentioned before, you need to come to grips with this on your own terms. Us telling you about it won't make it any more intuitive to you. People have trouble with imaginary numbers, but I can't make them comfortable with them by saying words. Only them working with the math will let them feel comfortable and understand what is happening. Same with negative numbers. Some people don't feel comfortable with them and don't think they have meaning. If i owe you -5 marbles, then really you owe me +5 marbles. But, if I say i have -5 marbles, what does that mean?

 

[steveB]

PG,

Here is some additional information on negative frequency. I think we've hit the major points in discussing here, but it can be useful to read more detailed descriptions in which much more thought has been put into the explanations. For example, this PDF is interesting.

https://www.electro-tech-online.com/custompdfs/2013/08/205.pdf

Also, I did find one discussion that hit a point we didn't bring up here, which is the symmetry of time reversal. The idea here is that Fourier theory in not a physical theory that tried to identify a forward flow of time and therefore it can't say anything special about the positive direction of time versus the negative direction of time. Hence, positive and negative frequency is needed to keep the symmetry. This is the closest explanation that borders on a physical interpretation that I've seen. I found this in the following reference.

https://dsp.stackexchange.com/quest...physical-significance-of-negative-frequencies

And the following excerpt is relevant.

The physical interpretation of negative frequencies is as follows:
My first realization was that fourier is time-agnostic. That is, if you think about it, there is nothing in fourier analysis or the transform itself that can tell you what the 'direction' of time is. Now, imagine a physically oscillating system (ie a real sinusoid from say, a current over a wire) that is oscillating at some scalar temporal-frequency, f.
Imagine 'looking' down this wave, in the forwards direction of time as it progresses. Now imagine calculating its difference in phase at every point in time you progress further. This will give you your scalar temporal frequency, and your frquency is positive. So far so good.
But wait a minute - if fourier is blind to time, then why should it only consider your wave in the 'forward' time direction? There is nothing special about that direction in time. Thus by symmetry, the other direction of time must also be considered. Thus now imagine 'looking' up at the same wave, (ie, backwards in time), and also performing the same delta-phase calculation. Since time is going backwards now, and your frequency is change-of-phase/(negative time), your frequency will now be negative!
What Fourier is really saying, is that this signal has energy if played forward in time at frequency bin f, but ALSO has energy if played backwards in time albeit at frequency bin -f. In a sense it MUST say this because fourier has no way of 'knowing' what the 'true' direction of time is!
So how does fourier capture this? Well, in order to show the direction of time, a rotation of some sort must be employed such that a clockwise roation dealinates 'looking' at the signal in the forward arrow of time, and a counterclockwise roation dealinates 'looking' at the signal as if time was going backwards. The scalar temporal frequency we are all familiar with should now be equal to the (scaled) absolute value of our vector angular frequency. But how can a point signifying the displacement of a sinusoid wave arrive at its starting point after one cycle yet simultaneously rotate around a circle and maintain a manifestation of the temporal frequency it signifies? Only if the major axes of that circle are composed of measuring displacement of this point relative to the original sinusoid, and a sinusoid off by 90 degrees. (This is exactly how fourier gets his sine and cosine bases the you project against every time you perform a DFT!). And finally, how do we keep those axes seperate? The 'j' guarantees that the magnitude on each axis is always independant of the magnitude on the other, since real and imaginary numbers cannot be added to yield a new number in either domain. (But this is just a side note).
Thus in summary:
The fourier transform is time-agnostic. It cannot tell the direction of time. This is at the heart of negative frequencies. Since frequency = phase-change/time, anytime you take the DFT of a signal, fourier is saying that if time was going forwards, your energy is located on the +ve frequency axis, but if your time was going backwards, your energy is located on the -ve frequency axis.
As our universe has shown before, it is precisely because Fourier does not know the direction of time, that both sides of the DFT must be symmetric, and why the existence of negative frequencies are necessary and in fact very real indeed.