Time-frequency and time-scale methods. Adaptive decompositions, uncertainty principles, and sampling

zbMath1079.42027MaRDI QIDQ1768511

Publication date: 15 March 2005

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

wavelets sampling Fourier transform Schrödinger operators windowed Fourier transform Zak transform Wigner distribution time-frequency analysis wavelet packets uncertainty principles time-scale analysis Balian-Low theorem Gabor systems adaptive decomposition

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sampling theory, sample surveys (62D05) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical methods for wavelets (65T60) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) General harmonic expansions, frames (42C15) Fourier series and coefficients in several variables (42B05) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Sampling theory in information and communication theory (94A20) General mathematical topics and methods in quantum theory (81Qxx) Nontrigonometric harmonic analysis (42Cxx)

Related Items (24)

Affine frame decompositions and shift-invariant spaces ⋮ Design of time-frequency optimal three-band wavelet filter banks with unit Sobolev regularity using frequency domain sampling ⋮ Filtered Gradient Algorithms for Inverse Design Problems of One-Dimensional Burgers Equation ⋮ On a (no longer) new Segal algebra: a review of the Feichtinger algebra ⋮ On support properties of functions and their Jacobi transform ⋮ Uncertainty principles for the Hankel transform ⋮ The homogeneous approximation property and localized Gabor frames ⋮ Uncertainty inequalities for the Heisenberg group ⋮ Optimization in the construction of cardinal and symmetric wavelets on the line ⋮ On the computation of the polar FFT ⋮ Uncertainty inequality for Radon transform on the Heisenberg group ⋮ Schmidt decomposable products of projections ⋮ Uncertainty principles for the coupled fractional Wigner distribution ⋮ On a progress in the Kontorovich–Lebedev transform theory and related integral operators ⋮ Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions ⋮ Uncertainty in time-frequency representations on finite Abelian groups and applications ⋮ Time–frequency concentration of the windowed Hankel transform ⋮ Toeplitz localization operators: spectral functions density ⋮ Uncertainty principles and time frequency analysis related to the Riemann-Liouville operator ⋮ Uniqueness results in an extension of Pauli's phase retrieval problem ⋮ Uncertainty principle of complex-valued functions in specific free metaplectic transformation domains ⋮ Uncertainty principles for the windowed Hankel transform ⋮ Time-frequency localization and sampling of multiband signals ⋮ Non-translation-invariance and the synchronization problem in wavelet sampling

This page was built for publication: Time-frequency and time-scale methods. Adaptive decompositions, uncertainty principles, and sampling