An embedding approach to frequency-domain and subband adaptive filtering

Frequency-domain and subband implementations improve the computational effi ciency and the convergence rate of adaptive schemes. The wen-known multidel ay adaptive filter (MDF) belongs to this class of block adaptive structures and is a DFT-based algorithm. In this paper, we develop adaptive structure s that are based on the trigonometric transforms DCT and DST and on the dis crete Hartley transform (DHT). As a result, these structures involve only r eal arithmetic and are attractive alternatives in cases where the tradition al DFT-based scheme exhibits poor performance. The filters are derived by f irst presenting a derivation for the classical DFT based filter that allows us to pursue these extensions immediately The approach used in this paper also provides further insights into subband adaptive filtering.