### Abstract

The discrete wavelet transform (DWT) is usually carried out by filter bank iteration, however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time-localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time-localization. The basis, is not based on filter bank iteration, instead different filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches 2/3 that of the corresponding functions obtained by filter bank iteration. This slantlet basis is piecewise linear and retains the octave-band characteristic. Closed form expressions for the filters are given and improvement in a denoising example is shown. This bases, being piecewise linear, is reminiscent of the slant transform, to which it is compared.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |

Publisher | IEEE |

Pages | 53-56 |

Number of pages | 4 |

State | Published - 1998 |

Event | Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Pittsburgh, PA, USA Duration: Oct 6 1998 → Oct 9 1998 |

### Other

Other | Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |
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City | Pittsburgh, PA, USA |

Period | 10/6/98 → 10/9/98 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis*(pp. 53-56). IEEE.

**Slantlet transform.** / Selesnick, Ivan.

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

*Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.*IEEE, pp. 53-56, Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Pittsburgh, PA, USA, 10/6/98.

}

TY - GEN

T1 - Slantlet transform

AU - Selesnick, Ivan

PY - 1998

Y1 - 1998

N2 - The discrete wavelet transform (DWT) is usually carried out by filter bank iteration, however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time-localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time-localization. The basis, is not based on filter bank iteration, instead different filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches 2/3 that of the corresponding functions obtained by filter bank iteration. This slantlet basis is piecewise linear and retains the octave-band characteristic. Closed form expressions for the filters are given and improvement in a denoising example is shown. This bases, being piecewise linear, is reminiscent of the slant transform, to which it is compared.

AB - The discrete wavelet transform (DWT) is usually carried out by filter bank iteration, however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time-localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time-localization. The basis, is not based on filter bank iteration, instead different filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches 2/3 that of the corresponding functions obtained by filter bank iteration. This slantlet basis is piecewise linear and retains the octave-band characteristic. Closed form expressions for the filters are given and improvement in a denoising example is shown. This bases, being piecewise linear, is reminiscent of the slant transform, to which it is compared.

UR - http://www.scopus.com/inward/record.url?scp=0031639451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031639451&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0031639451

SP - 53

EP - 56

BT - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis

PB - IEEE

ER -