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Abstract-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. In this paper, we develop adaptive structures that are based on the trigonometric transforms DCT and 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.

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This paper solves the problem of designing recursive-least-squares (RLS) lattice (or order-recursive) algorithms for adaptive filters that do not involve tapped-delay-line structures. In particular, an RLS-Laguerre lattice filter is obtained.

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The existing derivations of conventional fast RLS adaptive filters are intrinsically dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. In this paper, we show, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures. We show that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormallybased models. One of the benefits of working with orthonormal bases is that fewer parameters can be used to model long impulse responses.