IIR filter
A digital filter that feeds its own output back in — cheap to compute, a close cousin of analogue circuits, and perfectly capable of blowing up if you get the maths wrong.
Because of the feedback, the impulse response in theory never ends — hence infinite. The workhorse is the biquad: two poles, two zeros, five coefficients. Chain a handful and you have a full parametric equalizer for a fraction of what an FIR filter costs, with essentially no latency. Robert Bristow-Johnson's Audio EQ Cookbook, a plain text file from the 1990s, is still where a surprising amount of commercial code gets its coefficients.
The catch is phase: different frequencies are delayed by different amounts, just as in an analogue EQ — which plenty of engineers consider a feature rather than a flaw. Rounding errors in the feedback path can make the filter unstable, though, especially in fixed-point arithmetic at low frequencies.