How is information encoded in an electrical/radio signal at the stage of an emitting station then correctly recovered at the stage of the receiver?
There are a number of ways this can be achieved in radio, but in all of them you create a carrier wave (that’s what gives the frequency) and modulate information on to it.
The carrier wave is a sine wave and is a function of alternating cycles over time. It looks like this:
There’s no information modulated on there yet, though. The idea is that you measure a cycle as from adjacent feature to the next. Above you see an amplitude going up and down, and if we started where the diagram does, we see the amplitude rising, going back down to the centre, dropping under the centre, and going down and back up to the centre. That’s one cycle, and there’s two depicted on there if you look. The number of cycles in a given time (usually one second) is the frequency, and one cycle per second is 1 Hz. In radio comms, if you make the frequency large enough, you can make electromagnetic waves propagate from an antenna. One like this, with no information on it, could be used as a binary system, for transmitting Morse Code. That would be called On-Off Keying (OOK) and if the wave is there it’s 1 and if not 0.
To get this wave you need an oscillator. That can be made from a circuit consisting of an inductor and capacitor, or a quartz crystal, or anything that can produce the sine wave; these days ASIC chips to which you attach the required size of inductor can be bought. Once you’ve done that, you amplify and send it through the antenna, making sure your antenna and power amplifier are matched properly or you’ll blow things up.
The next simplest way is to modulate a signal on there. When Fessenden did the first amplitude modulations he used a Westinghouse generator to produce the carrier, and put a carbon microphone in the line, and amplified the lot and threw it out of the antenna. The lot could be heard through a Marconi system using coherors but it was all over the spectrum and such a thing wouldn’t be legal today. AM limits what it can broadcast to 4.5kHz audio and filters are used to limit interference. The output looks like this:
You don’t need much to detect AM. Troops used to do it with a pair of high impedance headphones and an oxidised razor blade. You can get a reliable reception with two pieces of wire, an inductor, two capacitors and a germanium diode, and if you want to amplify an op-amp and a transistor stage can be used to drive a speaker (you’ll need a power source for that, such as batteries).
Next along was frequency modulation (FM), invented almost single-handedly by Major Edwin Armstrong. He was remarkable- there aren’t many people that can revolutionise their fields once, let alone multiple times. FM uses a carrier wave and a modulating single, but the amplitude does not vary. You shift very slightly the frequency and get a ratio; you can do this with a signal transistor and a tank circuit, and a couple of capacitors to stop DC at your inputs, and again ASIC chips exist for the purpose nowadays. A commercial one will contain all sorts of filters and other whistles and bells. The output will look like this:
Detecting an FM signal is almost always done by a superhetorodyne receiver. In easy steps, it works like this: the signal coming in through the antenna is filtered by a tank and the required frequency is accepted and anything else rejected. What we want is sent to an RF amplifier and the output from the RF amplifier and a local oscillator in the receiver is mixed. This gives us an intermediate frequency (IF) which by convention is 10.7 MHz (but it doesn’t have to be). IF is amplified and passed through to a detector which detects the ratio of shift and recovers the audio component. You could also have an envelope detector, these are simpler but you lose a lot of the quality of sound. The audio is passed to an audio amplifier and finally the speaker(s). The local oscillator and the tank are on a ganged tuner and automatic gain control is sent from the detector to the preceding stages as a kind of feedback.
The above two are analogue systems, and modern comms are often done with digital ones. There are a number of methods here. The most often seen is QAM (quadrature amplitude modulation). This is incredibly complex and involves splitting up the carrier into orthagonal parts, sending information simultaneously and recombining it at the end.