The FCC controls something on the order of 10 $kHz$ and 2.75 $GHz$. The frequency band is in the control of the FCC like public land. The FCC sells frequency ranges. Radio stations and cable companies pay for that, and in the end, that frequency spectrum belongs to you and me.


\emph{Frequency Division Multiplexing} enables simultaneous transmission of multiple signals. 


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\rput(5.5,2.25){$y(t)$}

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\rput(2.75,0.5){$cos(\omega_2t)$}

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\rput(2.75,2){$cos(\omega_1t)$}


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We can multiply each incoming signal by a mutually orthogonal functions, in this case we use the cosine function with frequencies $\omega_1, \omega_2, \dots, \omega_n$. So, you have a frequency spectrum, you split it into different ranges and distribute different frequency bands to different stations. Let's say we are talking about three radio stations. So, you have multiple signals awaiting transmission:

% \img{images/modulators/freqdiv/stations/justd.ps}
% \img{images/modulators/freqdiv/stations/justamadou.ps}
% \img{images/modulators/freqdiv/stations/justbabak.ps}

What happens when we use frequency division multiplexing? We get the following spectra for $Y(\omega)$:

% \img{images/modulators/freqdiv/stations/all.ps}

How would we get a particular station? Lets suppose we want to get the station at $\omega_2$. A crude solution would be to use a band pass filter. At the receiver, lets say you have a knob, and by turning that knob you determine which frequency you are interested in, which station. So, with that knob you would have to control, not only this frequency, but also this band-pass filter. For practical reasons building a band pass filter with that high frequency cutoff when these frequency bands are so close together, it's like city of Berkeley, there is no empty land. Lots of homes are small, and they are all tightly connected to each other---there is not a whole lot of wiggle room. This is an ideal band pass filter. Things have to roll out. The higher you go on frequency band the more difficult it is for circuit designers to build band pass fillers.


There has got to be another solution. Your knob will control the local oscillator, and maps whatever part of the spectrum you are interested in to one intermediate frequency. Then you have only one band pass filter for which you can design a filter and pass that through. So, regardless of where you are in the spectrum, by tuning the knob you mapped and grab this part and map it to that intermediate frequency. Grab the region around that intermediate frequency, and you have got a built-in band pass filter already. Then you demodulate. When the knob is tuned to a particular frequency, the circuit shifts it to a fixed intermediate frequency that is well within the range of our filter---not necessarily baseband but maps it to something close to zero.  
