Biquad filter
The building block of digital audio filtering: a recursive second-order filter with five coefficients that can be a lowpass, highpass, bandpass or EQ band.
The name comes from the transfer function being a ratio of two quadratics — two zeros and two poles. Each output sample is computed from the last three input samples and the last two outputs: five multiplies and a few adds. Robert Bristow-Johnson's Audio EQ Cookbook from the 1990s collected the formulas for turning frequency, Q and gain into coefficients, and that text file lives inside practically every equaliser written since.
Steeper filters are built by cascading several biquads rather than computing one higher-order filter directly — it is numerically far more stable. Like every IIR filter, a biquad shifts phase by different amounts at different frequencies.