### Abstract

2-band paraunitary FIR filter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets. The filter design problem is formulated and solved (a) as a constrained L_{∞} optimization problem and (b) as a constrained L_{2} optimization problem which allows arbitrary compromises between an L_{2} and an L_{∞} approach with both of them as special cases. Additional flatness constraints can also be easily included. The L_{2} and the L_{∞} design are based on the Kuhn-Tucker (KT) conditions and the alternation theorem, respectively. Therefore, optimality of the solution is guaranteed. The method (a) is a simpler alternative to a known method. The method (b) solves a more general problem than the approaches known in the literature including all of them as special cases.

Original language | English (US) |
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Title of host publication | IEEE Digital Signal Processing Workshop |

Editors | Anon |

Publisher | IEEE |

Pages | 211-214 |

Number of pages | 4 |

State | Published - 1994 |

Event | Proceedings of the 1994 6th IEEE Digital Signal Processing Workshop - Yosemite, CA, USA Duration: Oct 2 1994 → Oct 5 1994 |

### Other

Other | Proceedings of the 1994 6th IEEE Digital Signal Processing Workshop |
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City | Yosemite, CA, USA |

Period | 10/2/94 → 10/5/94 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*IEEE Digital Signal Processing Workshop*(pp. 211-214). IEEE.

**Constrained FIR filter design for 2-band filter banks and orthonormal wavelets.** / Lang, M.; Selesnick, Ivan; Odegard, J. E.; Burrus, C. S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE Digital Signal Processing Workshop.*IEEE, pp. 211-214, Proceedings of the 1994 6th IEEE Digital Signal Processing Workshop, Yosemite, CA, USA, 10/2/94.

}

TY - GEN

T1 - Constrained FIR filter design for 2-band filter banks and orthonormal wavelets

AU - Lang, M.

AU - Selesnick, Ivan

AU - Odegard, J. E.

AU - Burrus, C. S.

PY - 1994

Y1 - 1994

N2 - 2-band paraunitary FIR filter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets. The filter design problem is formulated and solved (a) as a constrained L∞ optimization problem and (b) as a constrained L2 optimization problem which allows arbitrary compromises between an L2 and an L∞ approach with both of them as special cases. Additional flatness constraints can also be easily included. The L2 and the L∞ design are based on the Kuhn-Tucker (KT) conditions and the alternation theorem, respectively. Therefore, optimality of the solution is guaranteed. The method (a) is a simpler alternative to a known method. The method (b) solves a more general problem than the approaches known in the literature including all of them as special cases.

AB - 2-band paraunitary FIR filter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets. The filter design problem is formulated and solved (a) as a constrained L∞ optimization problem and (b) as a constrained L2 optimization problem which allows arbitrary compromises between an L2 and an L∞ approach with both of them as special cases. Additional flatness constraints can also be easily included. The L2 and the L∞ design are based on the Kuhn-Tucker (KT) conditions and the alternation theorem, respectively. Therefore, optimality of the solution is guaranteed. The method (a) is a simpler alternative to a known method. The method (b) solves a more general problem than the approaches known in the literature including all of them as special cases.

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UR - http://www.scopus.com/inward/citedby.url?scp=0028744380&partnerID=8YFLogxK

M3 - Conference contribution

SP - 211

EP - 214

BT - IEEE Digital Signal Processing Workshop

A2 - Anon, null

PB - IEEE

ER -