论文信息 - Time-frequency localisation operators-a geometric phase space approach: II. The use of dilations

Time-frequency localisation operators-a geometric phase space approach: II. The use of dilations

Operators which localise both in time and frequency are constructed. They restrict to a finite time interval and cut off low as well as high frequencies (band-pass filters). Explicit expressions for eigenvalues and eigenfunctions (Laguerre functions) are given.

I. Daubechies | T. Paul

[1] D. Slepian,et al. Prolate spheroidal wave functions, fourier analysis and uncertainty — II , 1961 .

[2] H. Pollak,et al. Prolate spheroidal wave functions, fourier analysis and uncertainty — III: The dimension of the space of essentially time- and band-limited signals , 1962 .

[3] J. Klauder,et al. Unitary Representations of the Affine Group , 1968 .

[4] J. Klauder,et al. Continuous Representation Theory Using the Affine Group , 1969 .

[5] A. Grossmann,et al. Transforms associated to square integrable group representations. I. General results , 1985 .

[6] A. Grossmann,et al. TRANSFORMS ASSOCIATED TO SQUARE INTEGRABLE GROUP REPRESENTATION. 2. EXAMPLES , 1986 .

[7] Ingrid Daubechies,et al. Time-frequency localization operators: A geometric phase space approach , 1988, IEEE Trans. Inf. Theory.

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