The eigenvalues of matrices that occur in certain interpolation problems

IEEE Transactions on Signal Processing

Volumn 45, Issue 8, 1997, Pages 2115-2120

  Ferreira, Paulo J S G ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INTERPOLATION; MATRIX ALGEBRA; SET THEORY;

FINITE DIMENSIONAL INTERPOLATION PROBLEMS;

DIGITAL SIGNAL PROCESSING;

EID: 0031199631     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.611226     Document Type: Article

References (21)

1. A. Papoulis, "A new algorithm in spectral analysis and bandlimited extrapolation," IEEE Trans. Circuits Syst., vol. CAS-22, pp. 735-742, Sept. 1975.
2. R. W. Gerchberg, "Super-resolution through error energy reduction," Acta, vol. 21, no. 9, pp. 709-720, 1974.
3. D. C. Youla, "Generalized image restoration by the method of alternating orthogonal projections," IEEE Trans. Circuits Syst., vol. CAS-25, pp. 694-702, Sept. 1978.
4. D. C. Youla and H. Webb, "Image restoration by the method of convex projections: Part 1-Theory," IEEE Trans. Med. Imag., vol. MI-1, pp. 81-94, Oct. 1982.
5. M. I. Sezan and H. Stark, "Image restoration by the method of convex projections: Part 2-Applications and numerical results," IEEE Trans. Med. Imag., vol. MI-1, pp. 95-101, Oct. 1982.
6. H. J. Trussel and M. R. Civanlar, "The feasible solution in signal restoration," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP- 31, pp. 201-212, Apr. 1984.
7. R. G. Wiley, "Recovery of bandlimited signals from unequally spaced samples," IEEE Trans. Commun., vol. COMM-26, pp. 135-137, Jan. 1978.
8. F. A. Marvasti, M. Analoui, and M. Gamshadzahi, "Recovery of signals from nonuniform samples using iterative methods," IEEE Trans. Signal Processing, vol. 39, pp. 872-878, Apr. 1991.
9. K. Yao, "Applications of reproducing kernel Hubert spaces-Bandlimited signal models," Inform. Contr., vol. 11, pp. 429-444, 1967.
10. D. P. Kolba and T. W. Parks, "Optimal estimation for bandlimited signals including time domain considerations," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 113-122, Feb. 1983.
11. R. J. Marks, II, "Restoring lost samples from an oversampled bandlimited signal," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 752-755, June 1983.
12. P. Delsarte, A. J. E. M. Janssen, and L. B. Vries, "Discrete prolate spheroidal wave functions and interpolation," SIAM J. Appl. Math., vol. 45, pp. 641-650, Aug. 1985.
13. P. J. S. G. Ferreira, "Incomplete sampling series and the recovery of missing samples from oversampled bandlimited signals," IEEE Trans. Signal Processing, vol. 40, pp. 225-227, Jan. 1992.
14. K. Gröchenig, "A discrete theory of irregular sampling," Linear Algebra Appl., vol. 193, pp. 129-150, 1993.
15. P. J. S. G. Ferreira, "Interpolation and the discrete Papoulis-Gerchberg algorithm," IEEE Trans. Signal Processing, vol. 42, pp. 2596-2606, Oct. 1994.
16. T. Strohmer, "On discrete bandlimited signal extrapolation," in Mathematical Analysis, Wavelets and Signal Processing: An International Conference on Mathematical Analysis and Signal Processing, vol. 190, Contemporary Mathematics, M. E. H. Ismail, M. Z. Nashed, A. I. Zayed, and A. F. Ghaleb, Eds. Providence, RI: Amer. Math. Soc., 1995, pp. 323-337.
17. P. J. S. G. Ferreira, "Interpolation in the time and frequency domains," IEEE Signal Processing Lett., vol. 3, pp. 176-178, June 1996.
18. "Noniterative and faster iterative methods for interpolation and extrapolation," IEEE Trans. Signal Processing, vol. 42, pp. 3278-3282, Nov. 1994.
19. "The stability of a procedure for the recovery of lost samples in bandlimited signals," Signal Process., vol. 40, no. 3, pp. 195-205, Dec. 1994.
20. D. S. Chen and J. P. Allebach, "Analysis of error in reconstruction of two-dimensional signals from irregularly spaced samples," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 173-180, Feb. 1987.
21. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1990.