Bandwith of frequency division multiplexing (FDM bandwith)

[pinsky]

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 [f-f_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?

 

[f95toli]

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?

They shouldn't need thousands of modulators. I don't know much about DSSS, but presumably they just downconvert the signal (using a LO at f ) down to DC (well, LF) using a mixer and then they feed the resulting signal into a DSP, which then does the rest using FFT etc.

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

 

[sophiecentaur]

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 [f-f_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.


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?

If the channel is carrying information (if the carrier is being modulated at all) then its spectrum will not be a "vertical line". The channel will occupy some spectrum space - to include the carrier and its sidebands, depending on the data rate and the filtering used. In fact, the carrier itself will not be there if the modulation system is an efficient one.
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.

 

[pinsky]

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

If the channel is carrying information (if the carrier is being modulated at all) then its spectrum will not be a "vertical line".

, which is good since that what you pointed is essentially what bothers me.

So, let's 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 let's say 10 bits. I apply the DSSS chipping sequence, and now my signal is, let's 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 each other. Something like this:

[PLAIN]http://img411.imageshack.us/img411/8297/screenshotl.gif [Broken]

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, let's 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?

 

[sophiecentaur]

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?

 

[pinsky]

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?

 

[sophiecentaur]

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?

Yes - talking in terms of carriers alone doesn't give anything like the complete picture. Many modulation systems don't even have a carrier as such - take SSB, for instance.
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.

 

[pinsky]

I got it now. The answer came through the study of Information theory, a bit expectantly.
I was mostly

All the Fourier transform does is to relate the signal in the time domain with the signal in the frequency domain.

That's true, but after a modulation has been done, it gives me the amount of bandwidth.
I will draw the the figures soon as soon i get costumed to octave :)

 

[sophiecentaur]

That's true, but after a modulation has been done, it gives me the amount of bandwidth.
I will draw the the figures soon as soon i get costumed to octave :)

What you have written may not be correct (I may just have misunderstood you, though).

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 realized this but I am just making sure.