Ten lectures on wavelets
Multirate systems and filter banks
Multirate systems and filter banks
Time-frequency analysis: theory and applications
Time-frequency analysis: theory and applications
Digital Signal Processing
High-selectivity filter banks for spectral analysis of music signals
EURASIP Journal on Applied Signal Processing
Overcomplete discrete wavelet transforms with rational dilation factors
IEEE Transactions on Signal Processing
An Implementation of Rational Wavelets and Filter Design for Phonetic Classification
IEEE Transactions on Audio, Speech, and Language Processing
An orthogonal family of quincunx wavelets with continuously adjustable order
IEEE Transactions on Image Processing
Isotropic polyharmonic B-splines: scaling functions and wavelets
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Theory, implementation and applications of nonstationary Gabor frames
Journal of Computational and Applied Mathematics
Tunable-Q contourlet-based multi-sensor image fusion
Signal Processing
A frame based shrinkage procedure for fast oscillating functions
Computational Statistics & Data Analysis
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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 time-frequency 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.