The MDCT (Modified Discrete Cosine Transform) is the mathematical engine at the core of almost every lossy audio codec — MP3, AAC, Opus's CELT layer, AC-3, Vorbis. It converts short overlapping blocks of samples from the time domain into a frequency-domain representation, where the psychoacoustic model can decide how many bits each frequency band deserves and where masked detail can be quantized away. Its defining feature is the overlap: consecutive blocks share half their samples and cancel each other's edge artefacts on reconstruction (time-domain aliasing cancellation), avoiding the clicks a naive block transform would create. Window-length switching lets it use long blocks for steady tones and short ones for sharp transients.
