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What if instead you hid an encrypted signal within an otherwise perfectly legible audio signal? Imagine a song being played. To the ear the song seems perfectly normal. But, unbeknownst to a casual listener, there is an encrypted signal embedded within the audio signal. For example, data could be embedded within a song by ever-so-slightly raising or lowering the pitch of a song multiple times per second. Then if you had a copy of the original file, software could compare the original file to the song transmitted over the radio. The locations where the pitch rose or fell could be noted, and the data could be retrieved. You could send encrypted data without anyone realizing you're sending encrypted data. To anyone else listening, it would simply sound like a song or other audio track being played.
Actually, this idea has some merit, because it already has examples in other mediums. It's technically referred to as "steganography."
A common example with computers is hiding text, files, or applications within an image file.
https://github.com/7thSamurai/steganography
In the example for how to use this simple Image Steganography tool, the user hides a ZIP files with the entire contents of the book Dr. Jekyll & Mr. Hyde into the example image.
I don't see why something similar couldn't be achieved with audio.
In fact, here's an article on some basic audio steganography methods.
https://sumit-arora.medium.com/audio-steganography-the-art-of-hiding-secrets-within-earshot-part-2-of-2-c76b1be719b3
Not an expert, but I'm not sure steganography would be compatible with analog lossy data transmission methods like ham radio. The examples you linked relate to digital lossless audio, where it's easy to hide the data in individual bits.
Its not too hard to set up most modern trancievers for digital modes, I think the harder part would be making the mode itself.