Frequency-domain and subband implementations improve the computational efficiency and the convergence rate of adaptive schemes. The well-known multidelay adaptive filter (MDF) belongs to this class of block adaptive structures and is a DFT-based algorithm. We develop adaptive structures that are based on the trigonometric transforms, discrete cosine transform (DCT) and discrete sine transform (DST), and on the discrete Hartley transform (DHT). As a result, these structures involve only real arithmetic and are attractive alternatives in cases where the traditional DFT-based scheme exhibits poor performance. The filters are derived by first 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.