Affine projection algorithms perform well for acoustic echo cancellation and adaptive equalization. Although these algorithms typically provide fast convergence, they are unduly complex when updating the weights of the associated adaptive filter. In this paper, we propose a new subband affine projection (SAP) algorithm and a facile method for its implementation. The SAP algorithm is derived by combining the affine projection algorithm and the subband adaptive structure with the maximal decimation. In the proposed SAP algorithm, the derived weight-updating formula for the subband adaptive filter has a simple form as compared with the normalized least mean square (NLMS) algorithm. The algorithm gives improved convergence and reduced computational complexity. The efficiency of the proposed algorithm for a colored input signal is evaluated experimentally.

Recently, DOAS (differential optical absorption spectroscopy) has been used for nondestructive air monitoring, in which the LS (least squares) method is used to calculate trace gas concentrations due to its computational simplicity. This paper applies the ICA (independent component analysis) method to the DOAS system of air monitoring, since the LS method is insufficient to recover the desired spectra perfectly due to sparsity characteristic. If the sparsity of reference spectra in the DOAS system imposes the assumption of independence, the ICA algorithm can be used. The proposed method is used to regress the observed spectrum on the estimates of the reference spectra. The ICA algorithm can be seen as a preprocessing method where the ICs of the references are used as the input in the regression. The performance of the proposed method is evaluated in simulation studies using synthetic data.