Abstract
This chapter introduces the Wiener statistical theory of linear filtering that is a reference for the study and understanding of adaptive methods shown below in the text.
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Notes
- 1.
It is noted that, in the complex case, for the filter’s output calculation can be also used the following notation \( y\left[n\right]={\left({\mathbf{w}}^T{\mathbf{x}}^{\ast}\right)}^{\ast }={\mathbf{x}}^T{\mathbf{w}}^{\ast }={\mathbf{x}}^T\widehat{\mathbf{w}} \), for \( \widehat{\mathbf{w}}={\mathbf{w}}^{*} \).
- 2.
® Matlab is a registered trademark of The MathWorks, Inc.
- 3.
We remind the reader that (∂x T a/∂x) = (∂a T x/∂x) = a and (∂x T Bx/∂x) = (B + B T)x. For vector and matrix derivative rules, see [1].
- 4.
The graphs in the figure are drawn by means of the ® Matlab mesh functions.
- 5.
To avoid possible ambiguity, we use the acronym AIC for adaptive noise/interference cancellation and ANC for active noise cancellation or control.
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Uncini, A. (2015). Optimal Linear Filter Theory. In: Fundamentals of Adaptive Signal Processing. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02807-1_3
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DOI: https://doi.org/10.1007/978-3-319-02807-1_3
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