Adaptive discrete cosine transform for feedback active noise control

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.