## Frequency-domain design of overcomplete rational-dilation wavelet transforms (2009)

Venue: | IEEE Trans. on Signal Processing |

Citations: | 6 - 1 self |

### BibTeX

@ARTICLE{Bayram09frequency-domaindesign,

author = {Ilker Bayram and Ivan W. Selesnick},

title = {Frequency-domain design of overcomplete rational-dilation wavelet transforms},

journal = {IEEE Trans. on Signal Processing},

year = {2009}

}

### OpenURL

### Abstract

The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Q-factor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Q-factors (desirable for processing oscillatory signals) or the same low Q-factor of the dyadic wavelet transform. The new wavelet transform is modestly overcomplete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible ‘constant-Q’ discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L2(R). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the timefrequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform’s redundancy and the flexibility allowed by frequency-domain filter design. I.