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Hi @Puppeteer, here is a basic explanation of a 1-pole IIR filter. IIR implies that feedback from the output is combined with the input signal so that the output signal never completely decays i.e. “infinite impulse”. If you want a more detailed explanation, this book is an invaluable resource (although I admittedly understand only a fraction of it). Basically this allows the creation of digital filters that more closely model what would be happening with resistor-capacitor networks in analog filters.

As far as I know, you are correct that resonance doesn’t happen in a 1-pole filter, but that doesn’t mean that there can’t be feedback in the equation used to produce the filter’s response.

Hope this helps!