Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of bi...

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Veröffentlicht in:	IEEE transactions on signal processing 2009-09, Vol.57 (9), p.3411-3425
Hauptverfasser:	Chaudhury, K.N., Unser, M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analytic signal Applied sciences Approximation B-spline multiresolution biorthogonal wavelet basis Concrete Construction Continuous wavelet transforms Detection, estimation, filtering, equalization, prediction directional Hilbert transform Discrete wavelet transforms dual-tree complex wavelet transform Exact sciences and technology Fast Fourier transforms Filter bank Fourier transforms Gabor filters Gabor function Heat treatment Hilbert transform Information, signal and communications theory Mathematical analysis Methodology Miscellaneous Multidimensional systems Signal and communications theory Signal processing Signal, noise Spline Splines Studies Telecommunications and information theory time-frequency localization Transforms Wavelet Wavelet analysis Wavelet transforms
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