Sampling in shift-invariant spaces with Gaussian generator

Sampling Theory in Signal and Image Processing

Volumn 6, Issue 1, 2007, Pages 71-86

  Hammerich, Edwin ^a  

^a Federal Ministry of Defence   (Germany)

Author keywords

Dual function; Exponential Sobolev space; Gauss transform; Gaussian function; Generator; Interpolating function; Interpolation theorem; Jacobi theta functions; Sampling theorem

Indexed keywords

EID: 33846305782     PISSN: 15306429     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. I. Daubechies, Time-frequency localization operators: A geometric phase space approach, IEEE Rans. Inform. Theory, 34, 605-612, 1988.
2. K. Gröchenig, Foundations of time-frequency analysis, Birkhäuser, Boston, 2001.
3. K. Gröchenig, Nonuniform sampling in shift-invariant spaces and localized frames, in: CD of International Workshop Samp TA05 - Sampling Theory and Applications (Samsun, July 10-15, 2005).
4. E. Hammerich, A sampling theorem for time-frequency localized signals, Sampl. Theory Signal Image Process., 3, 45-81, 2004.
5. A. J. Jerri, The Shannon sampling theorem - Its vaxious extensions and applications: A tutorial review, Proc. IEEE, 65, 1565-1596, 1977.
6. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and theorems for the special functions of mathematical physics, Springer-Verlag, Berlin, 1966.
7. M. Z. Nashed and G. G. Walter, General sampling theorems for functions in reproducing kernel Hilbert spaces, Math. Control, Signals, Syst., 4, 363-390, 1991.
8. C. E. Shannon, Communication in the presence of noise, Proc. IRE, 37, 10-21, 1949.
9. H. Triebel, Theory of function spaces, Birkhäuser Verlag, Basel, 1983.
10. M. Unser, Sampling - 50 years after Shannon, Proc. IEEE, 88, 569-587, 2000.
11. G. G. Walter, A sampling theorem for wavelet subspaces, IEEE Trans. Inform. Theory, 38, 881-884, 1992.
12. G. G. Walter and X. Shen, Wavelets and other orthogonal systems, Chapman & Hall/CRC, Boca Raton, 2001.
13. E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Univ. Press, London, 1963.
14. R. M. Young, An introduction to nonharmonic Fourier series, Academic Press, London, 1980.