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  • 1. Schüldt, Christian
    et al.
    Lindström, Fredric
    Li, Haibo
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
    Claesson, Ingvar
    Adaptive filter length selection for acoustic echo cancellation2009In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 89, no 6, p. 1185-1194Article in journal (Refereed)
    Abstract [en]

    The number of coefficients in an adaptive finite impulse response filter-based acoustic echo cancellation setup is an important parameter, affecting the overall performance of the echo cancellation. Too few coefficients give undermodelling and too many cause slow convergence and an additional echo due to the mismatch of the extra coefficients. This paper proposes a method to adaptively determine the filter length, based on estimation of the mean square deviation. The method is primarily intended for identifying long non-sparse systems, such as a typical impulse response from an acoustic setup. Simulations with band limited flat spectrum signals are used for verification, showing the behavior and benefits of the proposed algorithm. Furthermore, off-line calculation using recorded speech signals show the behavior in real situations and comparison with another state-of-the-art variable filter length algorithm shows the advantages of the proposed method.

  • 2. Zhou, Zhiyong
    et al.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On q-ratio CMSV for sparse recovery2019In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 165, p. 128-132Article in journal (Refereed)
    Abstract [en]

    As a kind of computable incoherence measure of the measurement matrix, q-ratio constrained minimal singular values (CMSV) was proposed in Zhou and Yu (2019) to derive the performance bounds for sparse recovery. In this paper, we study the geometrical properties of the q-ratio CMSV, based on which we establish new sufficient conditions for signal recovery involving both sparsity defect and measurement error. The ℓ1-truncated set q-width of the measurement matrix is developed as the geometrical characterization of q-ratio CMSV. In addition, we show that the q-ratio CMSVs of a class of structured random matrices are bounded away from zero with high probability as long as the number of measurements is large enough, therefore these structured random matrices satisfy those established sufficient conditions. Overall, our results generalize the results in Zhang and Cheng (2012) from q=2 to any q ∈ (1, ∞] and complement the arguments of q-ratio CMSV from a geometrical view.

  • 3.
    Zhou, Zhiyong
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sparse recovery based on q-ratio constrained minimal singular values2019In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 155, p. 247-258Article in journal (Refereed)
    Abstract [en]

    We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for the measurement matrices. With high probability, the developed measures for subgaussian random matrices are bounded away from zero as long as the number of measurements is reasonably large. Comparing to the restricted isotropic constant based performance analysis, the arguments in this paper are much more concise and the obtained bounds are tighter. Numerical experiments are presented to illustrate our theoretical results.

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