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On the Performance Analysis of Normalized Subband Adaptive Filtering Algorithm with Sparse Subfilters

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Abstract

Subband adaptive filtering algorithms can increase the convergence rate of system identification tasks when the input signal is colored. Recently, a new normalized subband adaptive filtering algorithm with sparse subfilters (NSAF-SF) has been proposed, whose main advantage is the lower computational complexity when compared to state-of-the-art subband approaches, while maintaining similar convergence performance. In this paper, the first- and second-order stochastic analyses of the NSAF-SF algorithm are presented in order to provide predictions about its transient and steady-state performances. A relationship between the adaptive subband coefficients and the ideal fullband transfer function is derived, and the algorithm is proven to produce an asymptotically unbiased solution. In addition, a closed-form expression is obtained for the steady-state mean square deviation (MSD) of the subfilter coefficients. Although the proposed analyses use conventional assumptions of statistical independence, they do not assume a specific stochastic characteristic for the input signal (e.g., Gaussianity or whiteness). Transient and steady-state theoretical predictions of the MSD are confirmed by simulations.

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Notes

  1. In this paper, the lengths of the analysis and synthesis filters are supposed to be equal.

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Acknowledgements

The authors would like to thank CNPq, CAPES and FAPERJ.

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Authors and Affiliations

  1. Instituto Nacional da Propriedade Industrial, Rio de Janeiro, RJ, Brazil

    Pedro P. S. Xavier

  2. Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Petrópolis, RJ, Brazil

    Diego B. Haddad

  3. Electrical Engineering Program, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, 21945-970, Brazil

    Mariane R. Petraglia

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  1. Pedro P. S. Xavier
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  2. Diego B. Haddad
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  3. Mariane R. Petraglia
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Correspondence to Mariane R. Petraglia.

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This work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico and in part by Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro, Brazil.

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Xavier, P.P.S., Haddad, D.B. & Petraglia, M.R. On the Performance Analysis of Normalized Subband Adaptive Filtering Algorithm with Sparse Subfilters. Circuits Syst Signal Process 39, 5830–5847 (2020). https://doi.org/10.1007/s00034-020-01438-2

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