Speech enhancement and acoustic noise reduction are two important tasks where adaptive filtering algorithms emerge as a competitive solution. Unfortunately, in such applications the convergence rate of the system identification is hampered when the excitation data is highly correlated. Subband adaptive algorithms have been developed to address such issue. A recently proposed low‐complexity subband adaptive structure with sparse subfilters is generalised, in order to permit a non‐uniform filter bank structure. This generalisation brings additional flexibility to the resulting critically decimated adaptive structure, which allows one to adapt it to the idiosyncrasies of the application of interest without losing the perfect‐reconstruction property. A closed‐form solution for the optimal values that the adaptive coefficient should assume in order to accurately emulate a given impulse response is derived. Simulations reveal that the resulting algorithm may outperform recently published subband adaptive filtering algorithms, thereby requiring even less computational effort.
Normalised subband adaptive filtering algorithms have attracted attention due to their ability to present faster convergence in the case of coloured excitation data. The NSAF-SF scheme is an example of a state-of-the-art subband adaptive algorithm that demands a low computational burden. This Letter proposes a deterministic local optimisation approach with affine constraints whose result leads to an enhanced NSAF-SF updating mechanism. One of these constraints consists of a projection into a hyperplane derived from a relaxed ℓ 1-norm restriction, which provides a sparsity-promoting scheme. Such a constraint incorporates prior information into the (originally sparsity-agnostic) NSAF-SF. Such prior information concerns the energy concentration of the ideal transfer function that the adaptive filter intends to identify. Furthermore, the advanced optimisation problem is modified in order to make the advanced adaptive filter robust against impulsive noise. The simulations present a performance improvement for both transient and steady-state regions.
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