On the design of two channel perfect construction QMF filters.

*(English)*Zbl 1039.93042Quadratic mirror filters (QMF) are widely used in communication technology. A QMF consists of a pair of analysis and synthesis filters. The paper addresses odd degree QMF banks with two channels with multiple poles at \(z=-1\) which ensures regularity of the generated wavelet basis. The paper presents rapidly converging design methods for the FIR case and the IIR case as well. For FIR filters, it is shown that the design problem corresponds to the solution of an eigenvalue problem. For IIR filters, the proposed algorithm leads to a filter bank which can be interpreted as a generalized version of the known biorthogonal design. A version which allows combined amplitude and delay responses is also presented. All algorithms are illustrated by typical examples computed with Mathlab.

Reviewer: Rüdiger Hoffmann (Dresden)

##### MSC:

93C62 | Digital control/observation systems |

93E11 | Filtering in stochastic control theory |

94C05 | Analytic circuit theory |

65T60 | Numerical methods for wavelets |

##### Keywords:

quadratic mirror filters; perfect reconstruction; equiripple approximation; eigenvalue problem; biorthogonal design##### Software:

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\textit{A. I. Saleh} et al., Int. J. Circuit Theory Appl. 28, No. 3, 209--224 (2000; Zbl 1039.93042)

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