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Bandwith of frequency division multiplexing (FDM bandwith) 
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#1
Nov1111, 05:18 AM

P: 97

Hello there!
I have a problem with conteptual understanding of the bandwith od channels that use frequency division multiplexing. How i understand that FDM works: We have a transmitter that transmits on one frequency f and the receiver that listens on that frequency. They can communicate becouse the frequency is the same. That frequency in a spectral diagram looks like a vertical line at f. It is common ito draw FDM in spectral diagrams as areas representing a range between frequencies [ff_{r},f+f_{r}]. The size of f_{r} are ussualy very small a percent of f , so i interprete them as tolerance in a way that a receiver would detect a frequency at f+f_{r} just the same as f. The problem arises when the bandwith are drawn as wide areas on the spectrum graph (like in DSSS  Direct sequence spread spectrum) like in the picture here What does that imply on the side of modulators? That they have to have thousands of modulators to cover a bandwith of couple of MHz at the same time? 


#2
Nov1111, 09:34 AM

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PF Gold
P: 2,249

Note that you can get very wideband modulators (there are even 6 GHz IQ modulators with an IF BW of 1 GHz). 


#3
Nov1111, 09:37 AM

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Thanks
PF Gold
P: 12,157

In FDM, the individual channel occupancy will determine how much spectral space needs to be left between channels (their notional band centre). Depending on the coding and modulation that is used, the channels may be squeezed closer together for greater spectral efficiency but it all depends upon what adjacent channel levels (and the shaping) can be tolerated. This is just the same as in any transmission system where channels occupy the same physical space  TV and FM broadcasting have the same problems. One possible model could be just that You haven't actually specified where your FDM system would be used, though, so it is difficult to be sure what you are actually discussing. 


#4
Nov1311, 02:51 PM

P: 97

Bandwith of frequency division multiplexing (FDM bandwith)
Thank you for your answers.
I was mainly troubled by the image i posted in the previous thread and DSSS (Direct sequence spread spectrum). But now you,ve gotten my a bit more confused with So, lets talk about FDM together with DSSS (which is a spread spectrum method). It is the bandwith of the carrier signal which bothers me. I have a digital signal consisting of some lets say 10 bits. I apply the DSSS chipping sequence, and now my signal is, lets say 50 bits. Now i have to convert that digital signal to a analog signal. Ok, ill use FSK (Frequency Shift Keying) as my method. Now i have a low frequency analog signel which consists of 2 different frequencies that swithc between eachother. Something like this: So after that, what is left is to rise the frequency of this signal to a higher value for the needs of communication. So, we rise it to, lets say 2.4 GHz, and so our signal now occupies that frequency. What am I missing here? Where do other lines in the spectral graph come from? What is a spread spectrum here? 


#5
Nov1311, 03:21 PM

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PF Gold
P: 12,157

I am finding it difficult to decide what you're really discussing here. I am not sure that you are using the correct terms because you seem to be hopping from one thing to another.
You are asking a basic question about FSK and also a question about Spread Spectrum techniques. I can, however, answer your last question: " Where do other lines in the spectral graph come from?" You are assuming that there should only be a spectral line at each of the frequencies that your fsk switches between. The detail of the spectrum of an fsk signal will depend on the filtering used for the modulation / keying but just think of it in these terms. In the simplest FSK system, you have a lower frequency carrier that is being amplitude modulated (i.e. turned on and off with some binary digital signal) and you have a higher frequency carrier that is on when the other is off and off when the other is on. That is TWO AM signals. The spectrum of this will be two carriers with a whole set of sidebands, extending out as far as the highest frequency contained by the original data waveform. If the data is more or less random, this will give a flattish spectrum, extending out to and beyond the frequency corresponding to a sequence 010101010101010....... So, not two lines but two bands. In your diagram, the switching is 'phase continuous' at the changeover and the signal 'looks' well behaved (making a smooth transition between data bits but, at the switchover, the signal will have a kink in it, unless the filtering and timing are arranged just right, and this will also affect the spectrum. Alternatively, you can regard the fsk signal as FM, with the modulation being the binary data signal. The spectrum of an FM signal is a lot more complicated that for an AM signal and the sidebands extend infinitely in either direction. Again, nothing like just two lines at the switched frequencies. Does that help clear anything up for you? 


#6
Nov1511, 01:22 AM

P: 97

I think i'm getting the hang of it. We're dealing with bands instead of single lines (irrelevant of the modulation scheme) because of the Fourier transform of the modulated signal.
For example. the picture i posted for frequency modulation, the process of actually emitting the signal is Fourier transforming it, and than emitting each harmonic resulting a band instead of a line? 


#7
Nov1511, 03:12 AM

Sci Advisor
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PF Gold
P: 12,157

Describing the Modulation System as "Fourier Transforming" is not accurate. All the Fourier transform does is to relate the signal in the time domain with the signal in the frequency domain. There is nothing more significant about one domain than the other aamof. You could spend your whole life only dealing either in the time domain or in the frequency domain, if you really wanted to. It wouldn't be very convenient, which is why we use both domains! Modulation, otoh, is a process that produces a New Signal  not just another version of the original. 


#8
Nov2311, 07:51 AM

P: 97

I got it now. The answer came through the study of Information theory, a bit expectantly.
I was mostly I will draw the the figures soon as soon i get costumed to octave :) 


#9
Nov2311, 08:05 AM

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PF Gold
P: 12,157

It is not good enough, for anything other than simple AM, to Fourier transform the baseband signal of you want to find the occupied bandwidth of the modulation. You need to FT the resulting modulated signal. Modulation is NOT FT'ing by any stretch of the imagination. The two things are entirely different processes. The sidebands of an AM signal are just mirror images of the baseband signal, on either side of the carrier but the sidebands of an FM signal are infinite in extent for even the simplest (sinusoidal) modulating signal (Their amplitudes follow a Bessel Function aamof). Calculating the spectrum of a general FM signal can only really be done numerically. You may have realised this but I am just making sure. 


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