I've been puzzling how it is that you can tune into a signal on a particular frequency. How can it be possible to get rid of all the other signals that are added together? I don't know how much of this makes any sense, but I have tried to specify the problem mathematically. Suppose [tex]R_1(t), R_2(t), R_3(t)[/tex] are all functions of time that represent the audio going out on 3 radio stations. Suppose the carrier frequencies are [tex]f_1, f_2, f_3[/tex] respectively. Then the total signal [tex]R(t)[/tex] will be [tex]R(t) = R_1(t) \sin(2 \pi f_1 t) + R_2(t) \sin(2 \pi f_2 t) + R_3(t) \sin(2 \pi f_3 t)[/tex]. How is it that we can recover [tex]R_1(t), R_2(t), R_3(t)[/tex], only by sampling [tex]R(t)[/tex] and given that we know [tex]f_1, f_2, f_3[/tex]? What mathematical operation can we do to recover the signals? I believe for this to work [tex]R_1(t), R_2(t), R_3(t)[/tex] cannot carry frequencies higher than half their respective carrier frequencies. Is that right?