The theory and performance of adaptive discrete cosine transform filters for feedback active noise control (ANC) is examined. The discrete cosine transform filter is a realization of an FIR filter as the cascade of an all-zero FIR filter with a bank of IIR digital resonators. The result of such a realization is that each of the IIR resonators has a magnitude coefficient and a phase coefficient. Thus, each coefficient can be directly identified with an amplitude or phase of the transfer function at a particular frequency when run as an adaptive filter. The discrete cosine transform filter is used in a filter-X LMS implementation of a feedback active noise control system that uses a single error microphone and a single loudspeaker.