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Discrete Frequency Warped Wavelets: Theory and Applications
 IEEE Trans. Signal Processing
, 1998
"... In this paper, we extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discretetime by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of ..."
Abstract

Cited by 14 (7 self)
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In this paper, we extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discretetime by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions. We show that the discretetime warped wavelets lead to welldefined continuoustime wavelet bases, satisfying a warped form of the twoscale equation. The shape of the wavelets is not invariant by translation. Rather, the "wavelet translates" are obtained from one another by allpass filtering. We show that the phase of the delay element is asymptotically a fractal. A feature of the warped wavelet transform is that the cutoff frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure. The new transform provides an arbitrary tiling of the timefrequency plane, which can be designed by selecting as little as a single parameter. This feature is particularly desirable in cochlear and perceptual models of speech and music, where accurate bandwidth selection is an issue. As our examples show, by defining pitchsynchronous wavelets based on warped wavelets, the analysis of transients and denoising of inharmonic pseudoperiodic signals is greatly enhanced.
TimeVarying Frequency Warping: Results and Experiments
"... Dispersive tapped delay lines are attractive structures for altering the frequency content of a signal. In previous papers we showed that in the case of a homogeneous line with first order allpass sections the signal formed by the output samples of the chain of delays at a given time is equivalent ..."
Abstract

Cited by 2 (1 self)
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Dispersive tapped delay lines are attractive structures for altering the frequency content of a signal. In previous papers we showed that in the case of a homogeneous line with first order allpass sections the signal formed by the output samples of the chain of delays at a given time is equivalent to compute the Laguerre transform of the input signal. However, most musical signals require a timevarying frequency modification in order to be properly processed. Vibrato in musical instruments or voice intonation in the case of vocal sounds may be modeled as small and slow pitch variations. Simulations of these effects require techniques for timevarying pitch and/or brightness modification that are very useful for sound processing. In our experiments the basis for timevarying frequency warping is a timevarying version of the Laguerre transformation. The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay elem...