## Abstract

This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of BBZ. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.

Original language | English (US) |
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Article number | 5752263 |

Pages (from-to) | 3560-3575 |

Number of pages | 16 |

Journal | IEEE Transactions on Signal Processing |

Volume | 59 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2011 |

## Keywords

- Constant-Q transform
- Q-factor
- filter bank
- wavelet transform

## ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering