What's your confusion exactly?

Mathematics wise, there's not really a difference between the antenna picking out the signal versus the electronics afterwards needing to on the wire. What's your background? From the way you are talking it kind of sounds like you wouldn't understand how a simple low pass RC filter is able to separate the low frequencies while suppressing the high frequencies, or how a high-pass RC fitler is able to separate the high frequencies from the low frequencies. Are you familiar with Fourier?

I think my confusion is how two different frequency carrier signals can be on the same wire and distinguished by the receiver. It seems the waveform would not oscillate in its original form over the wire because of addition to a different waveform

@Nick Are you aware that when you modulate a signal, say a 20-20kHz audio signal onto a 100MHz carrier it no longer covers that original 20-20kHz range when it goes over the wire or on the air? Instead it now occupies the area around 100MHz spilled over a bit to either side.

+0.5 for finding a name battery-powered parallel to parallel 1:1 decoder drawn by Walwert that sounds like a Walwart power supply even if it not relevant

@DKNguyen yes the envelope

@Nick Then I don't really understand what your confusion is. The carrier modulated signals all cover unique frequencies which can be separated out with filters. The really weird stuff is the spread spectrum stuff where the frequencies are shared but the mathematics behind the codes used lets you separate it out. When you think about it, it's actually more amazing that you can hear two people speaking at the same time because those sound waves aren't on carriers at all and are actually overlapping frequencies.

@DKNguyen if you add two different signals together, as is being done in examples, how can each be separated? Won’t the waveform oscillate differently?

@Nick This is why I asked if you were familiar with Fourier. If you add a 1MHz sine wave with a 2MHz sine wave, regardless of phase shift you still mathematically know the constituents. Add in sine waves of a thousand more frequencies and they are all still in there and can be mathematically separated out. If you plotted the time graph it would look like noise to our eyes though (just like how audio graphs looks like noise) because your visual cortex isn't meant to interpret information like like. Your auditory cortex certainly can though.

Look at this example which is more structured so doesn't look like noise: en.wikipedia.org/wiki/Square_wave#/media/… In the graph that only has the fundamenta, 3rd, and 5th harmonic required to make a square wave (a true square wave with sharp edges and flat peaks and valleys requires infinite number of odd harmonics). Do you see how you can spot the three sine-waves hidden in there? The 3rd harmonic is the most difficult one to spot.

Two higher frequency sine waves look different phases. I think I need to read more about Fourier Transforms now

How much calculus do you know?

But it's simpler than a lot of these comments. Two or more signals (frequencies) in a linear system do not mix or combine. This is the key. And that's what a wire is - a linear system. At the receiver, you just need a way to separate, or differentiate between the various signals. If they are different in frequency, all you need, notionally, is just a bunch of bandpass filters each one tuned to the frequency of interest.

@user1850479 General theory and vector calculus, but I still need to use a CAS for some forms

@SteveSh when you say two different signals don’t mix or combine I’m confused. In above comments Dknguyen provides a square wave link which shows two frequencies added. I think it’s this waveform that is passed to a Fourier transform to differentiate the signals? Is the transform a band pass filter to which you refer?

Since two sinusoids with different frequency are orthogonal, you can always separate them with a dot product, same a the orthogonal components of a velocity or position vector. See: math.stackexchange.com/questions/474398/…

@user1850479 how are they orthogonal? Do you mean by phase?

@Nick No, he not phase. You just have to accept that sinusoids of different frequencies when added together do not become intermingle and become lost. They are all still there in their original form. Sinusoids of different frequencies are orthogonal in the same way basis vectors are orthogonal: unique, separable, independent, don't cross paths.

Take a look at the linked question, which explains how they are orthogonal.

@Nick - Yes, the 2 frequencies add in a sense. But they also separable at the destination. Back to th square wave for a moment. When someone generates square wave digitally, they do that just by switching a transistor, or pair of transistors ON and OFF. It's not done by combining a bunch a sine waves.

Plus, your old AM radio would never have worked if signals combined the way you think they do in a medium, like a wire. All of the stations picked up by the antenna are separable by the tuners and filters that follow.

@SteveSh that helps. What if the two frequencies added are in the form of square waves instead of a sinusoid which form the carrier frequencies. Can the transform still be used to demodulate the two carriers?

@DKNguyen what you say seems to imply an unlimited number of channels on the medium, but I know each channel has bandwidth so due to the spacing the number of channels is finite. Do you know what determines the channel width?

@Nick Did you miss my second comment when I said that when you modulate a 20Hz-20kHz signal it sits centered around the carrier frequency and spills a bit off to either side of it? A modulated signal isn't just the carrier. It's the sidebands around it that carry the data.

That picture is for Sömmerring's "telegraph." It generates bubbles at the receiving end. Nothing magical about it. Just electro-chem, which is why the battery stack at the other end. I've no idea at all why that picture was shown here as illustrating anything interesting with respect to the rest of the text in the question. I'm just mystified. And besides, there's been no mention at all of using a Bragg crystal for simultaneous separation of frequencies from an antenna, despite it being used for decades in the P3 aircraft.