## Adaptive IIR Filtering in Signal Processing and ControlIntegrates rational approximation with adaptive filtering, providing viable, numerically reliable procedures for creating adaptive infinite impulse response (IIR) filters. The choice of filter structure to adapt, algorithm design and the approximation properties for each type of algorithm are also addressed. This work recasts the theory of adaptive IIR filters by concentrating on recursive lattice filters, freeing systems from the need for direct-form filters.;A solutions manual is available for instructors only. College or university bookstores may order five or more copies at a special student price which is available upon request. |

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### Contents

Introduction | 1 |

Recursive Filter Structures | 31 |

The BeurlingLax Theorem Hankel Forms | 82 |

Rational Approximation in Hankel Norm | 145 |

Approximation | 180 |

Stability of TimeVarying Recursive Filters | 228 |

Gradient Descent Algorithms | 258 |

The SteiglitzMcBride Family of Algorithms | 374 |

### Common terms and phrases

adaptation algorithm adaptive filter adaptive IIR filtering algorithm all-pass function anti-causal bandwidth Chapter computed Consider constraint convergent point corresponding cost function deduce deg H(z denote differential equation direct form filter DM(z eigenvalues equation error error signal Example Figure filtered regressor function H(z gradient descent Grammian Hankel norm Hankel singular values hyperstability IEEE Trans impulse response inner product input sequence interpolation lattice algorithm lattice filter lattice form Lemma linear Lyapunov equation matrix minimize minimum phase minimum point noise-free notch filter notch frequency obtained optimal orthogonal orthonormal output error parameter trajectories pole-zero cancellations poles positive definite prefilter rational function recursion reduced error surface result rotation angles Schur complement Section Signal Processing sinusoid solution spectral density spectral density function stable and causal stationary point Steiglitz-McBride iteration subspace Suppose Szego polynomials Theorem time-varying time-varying system transfer function transformation undermodelled unit circle unknown system variance vector verify white noise yields zeros