MDCT (modified discrete cosine transform)
The overlapping frequency transform underneath almost every lossy audio codec since the 1990s.
A codec wants to chop audio into blocks and spend bits where the ear is listening, but hard block edges click. The MDCT uses blocks that overlap by half. Each block yields only half as many coefficients as it has samples, so the overlap costs nothing in data rate, and the aliasing it introduces in the time domain cancels out when neighbouring blocks are added together. John Princen and Alan Bradley published the principle, time-domain aliasing cancellation, in 1986–87.
Dolby Digital, MP3 (as a hybrid with a filter bank), AAC, Vorbis and Opus all rely on it. Its weak spot is pre-echo: quantisation noise spreads across the whole block, so a sharp drum hit arrives with a faint hiss in front of it. Codecs therefore switch to short blocks when a transient is coming.