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Block and Transform Domain Algorithms

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Fundamentals of Adaptive Signal Processing

Part of the book series: Signals and Communication Technology ((SCT))

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Abstract

In this chapter structures and algorithms for the implementation of adaptive filters (AF) with the purpose of improving the convergence speed and reducing the computational cost are presented. In particular, they are classified as block and online methods, operating in the time domain, in the transformed domain (typically the frequency domain), and in frequency subbands mode.

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Notes

  1. 1.

    In some sections of this chapter, for reasons of notation clarified in the following, the length of the filter is referred to as M F . The reader will note that generally the length of the filter is denoted by M, implying M F  = M.

  2. 2.

    The symbols x ⌈M⌉ and x ⌊L⌋ denote, respectively, the first M and the last L samples of the vector x.

  3. 3.

    In this section the filter length is referred to as M F .

  4. 4.

    The roots of the polynomial (1 − z −M) are uniformly placed around the unit circles exactly like the frequency-bins of a M points DFT.

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Authors and Affiliations

  1. DIET, Sapienza University of Rome, Rome, Italy

    Aurelio Uncini

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  1. Aurelio Uncini
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Uncini, A. (2015). Block and Transform Domain Algorithms. In: Fundamentals of Adaptive Signal Processing. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02807-1_7

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  • DOI: https://doi.org/10.1007/978-3-319-02807-1_7

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