Optimal wavelet design via multiresolutional parametric spectral estimation

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Abstract
Due to the fact that linearly dependent wavelet transforms are inefficient in computation and storage, the most popular discrete wavelet transforms (DWT) use orthonormal basis decompositions (ODWT). However, there are several problems related to ODWT: as a time- frequency analyzer, the time-frequency resolution and localization of ODWT are poor; from a spectral analysis point of view, the ODWT produces a distorted spectrum with energy leaking, aliasing, and magnitude distortion; to produce a reasonable time-varying spectrum, the signal is required to be octave-distributed with a spectral shape matching the spectra of the wavelets. To overcome these problems, a new approach for designing the optimal wavelet is proposed. Using the multiresolution parametric spectral estimator, the new method continuously tracks the time-varying signal to adapt the optimal wavelets, and yields high resolution, localization, and fidelity for the resulting time-frequency decomposition. When the optimal wavelets act as matched filters they can greatly reduce broadband background noise in the decomposition process.

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