论文信息 - Uncertainty Principles for Time-Frequency Operators - 字舞流文

Uncertainty Principles for Time-Frequency Operators

This paper explores some of the connections between classical Fourier analysis and time-frequency operators, as related to the role of the uncertainty principle in Gabor and wavelet basis expansions.

John J. Benedetto | Christopher Heil | David F. Walnut | D. Walnut | C. Heil | J. Benedetto

[1] Ingrid Daubechies,et al. Two theorems on lattice expansions , 1993, IEEE Trans. Inf. Theory.

[2] A. Janssen. Bargmann transform, Zak transform, and coherent states , 1982 .

[3] G. Battle. Heisenberg proof of the Balian-Low theorem , 1988 .

[4] Christopher Heil,et al. Continuous and Discrete Wavelet Transforms , 1989, SIAM Rev..

[5] Guy Battle. Phase space localization theorem for ondelettes , 1989 .

[6] I. Daubechies,et al. PAINLESS NONORTHOGONAL EXPANSIONS , 1986 .

[7] F. Low. Complete sets of wave packets , 1985 .

[8] Ingrid Daubechies,et al. The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[9] A. Cohen. Ondelettes, analyses multirésolutions et filtres miroirs en quadrature , 1990 .

[10] R. Balian. Un principe d'incertitude fort en théorie du signal ou en mécanique quantique , 1981 .

[11] Y. Meyer. Principe d'incertitude, bases hilbertiennes et algèbres d'opérateurs , 1986 .

[12] I. Daubechies. Orthonormal bases of compactly supported wavelets , 1988 .

[13] S. Mallat. Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[14] Dennis Gabor,et al. Theory of communication , 1946 .

[15] R. Tolimieri,et al. Abelian harmonic analysis, theta functions and function algebras on a nilmanifold , 1975 .

[16] R. Duffin,et al. A class of nonharmonic Fourier series , 1952 .