I see, so it was constantly broadcasting and then he’d encode some message in the signal to indicate if someone was up stairs, instead of only broadcasting when there was a message to send. That certainly would explain it.

That certainly exacerbated it, but arguably it's not even the worst RF sin being committed here. The other is spurious emissions. Toggling a GPIO at frequency f doesn't just result in frequency f, it also results in 3f, 5f, 7f, and so on because the GPIO is outputting a square wave not a sine wave. That's the best case. Unreliable timing could turn that from a frequency "comb" into a forest of spurs across the RF spectrum, and whichever spurs make it out of an antenna are going to break the law (best case) or interfere with important RF devices (worst case).

You're probably right that they used a guide like that. It seems irresponsible to publish that blog post. 99% of Pi tinkerers will read that disclaimer in the third paragraph and either not understand that life critical devices _do_ can be interfered with or think their use-case is special/low-powered and won't do any harm.

The irresponsible part is that he says you "must use a filter" if you attach an antenna but does not describe what that would entail. There's not even a link anywhere that would describe how to make a filter or even what he's talking about ("I have a filter... There's no bad power going into this thing!")

When you, "make something dangerous easy" you have a responsibility to be very specific in how to use your invention safely. Otherwise disaster seems inevitable.

You can buy razor blades almost everywhere for like a dollar.

(Reviewing this comment later I see it can be read in sort of a nasty way; my meaning was that we don't really assign blame to providers of dangerous tools, the low price of razor blades reflects this)

So they are generating a signal by toggling the IO pin on and off. Not only will there be a huge amount of harmonics, wouldn't processor interrupts wreak havoc on the output signal and cause even more interference?

Yes and no; if they're doing it right, they're using the DMA or PLL engine which runs independent of the main CPU/ALU. See https://github.com/F5OEO/PiFmRds "This version modulates the PLL instead of the clock divider for superior signal purity. The harmonics are unaffected, so the legal warning still applies."

Filtering this stuff isn't hard, but I'm realizing there aren't any good stone-simple tutorials for it. Might have to write one.

I've done a hobby project where I'm using pure RPi GPIO to drive a servo motor with PWM, so processor interrupts would ruin my day. So I can tell you that the rate at which modern Linux interrupts a running application is massively overstated. If your system is configured right, that happens maybe two or three times a second at most.

If you're running on a dedicated core, as you should, 99% of the time your application just happily runs along.

Can someone explain to me why generating a square wave creates lots of harmonics, as opposed to other kinds of waves?

The spectrum of a signal is its Fourier transform. Only sine and cosine signals have a "pure" signal with a single frequency. Anything else decomposes into a whole host of spectral contributions. Square waves are especially bad because they require contributions from infinitely many harmonics to produce the steep flanks. That is also why a clean square wave cannot exist: some kind of band limit is always present, resulting in ringing around the flanks.

See also Fourier Analysis on the Wikipedia article: https://en.m.wikipedia.org/wiki/Square_wave

Because you try to generate a square wave by adding toghether "round" waves (sinusoidal). In order to get into the "corners" you must add "round" waves with smaller and smaller diameters (period). Small periods means high frequencies. The more waves you add, the squarer the sum becomes.

A square wave IS the base frequency plus ALL[1] the odd harmonics (https://en.wikipedia.org/wiki/Square_wave#Fourier_analysis explains it better than I could).

[1]: Yes, so in reality you neither get an infinite set of harmonics, nor a perfect square wave.