An optimal basis of band-limited functions for signal analysis and design

IEEE Transactions on Signal Processing

Volumn 58, Issue 11, 2010, Pages 5744-5755

  Wei, Liying ^a   Kennedy, Rodney A ^a   Lamahewa, Tharaka A ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Fraction out of band energy (FOBE); Gabor's function; orthonormal basis; prolate spheroidal wave function (PSWF); time frequency

Indexed keywords

GABOR'S FUNCTION; ORTHONORMAL BASIS; OUT-OF-BAND; PROLATE SPHEROIDAL WAVE FUNCTIONS; TIME-FREQUENCY;

COMMUNICATION SYSTEMS; OPTIMIZATION; WAVE FUNCTIONS;

RADAR SYSTEMS;

EID: 79953818944     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2057427     Document Type: Article

References (32)

1. Q. Jin, Z. Q. Luo, and K. M. Wong, "An optimum complete orthonormal basis for signal analysis and design," IEEE Trans. Inf. Theory, vol. 40, no. 3, pp. 732-742, May 1994.
2. G. Lachs, "Optimization of signal waveforms," IEEE Trans. Inf. Theory, vol. IT-9, pp. 95-97, Apr. 1963.
3. D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-I," Bell Syst. Tech. J, vol. 40, pp. 43-63, Jan. 1961.
4. H. J. Landau and H. O. Pollack, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-II," Bell Syst. Tech. J., vol. 40, no. 1, pp. 65-84, Jan. 1961.
5. A. Papoulis, "Minimum-bias windows for high-resolution spectral estimates," IEEE Trans. Inf. Theory, vol. IT-19, no. 1, pp. 9-12, Jan. 1973.
6. D. Slepian, "On bandwidth," Proc. IEEE, vol. 64, no. 3, pp. 292-300, Mar. 1976.
7. A. Nuttall and F. Amoroso, "Minimum Gabor bandwidth ofMorthogonal signals," IEEE Trans. Inf. Theory, vol. 14, no. 5, pp. 440-444, July 1965.
8. A. Nuttall, "Minimum rms bandwidth of M time-limited signals with specified code or correlation matrix," IEEE Trans. Inf. Theory, vol. IT-14, no. 5, pp. 699-707, Sep. 1968.
9. D. Gabor, "Theory of communication," J. Inst. Elec. Eng., vol. 93, no. 26, pt. III, pp. 429-457, Nov. 1946.
10. L. C. Potter and K. S. Arun, "Energy concentration in band-limited extrapolation," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 7, pp. 1027-1041, Jul. 1989.
11. R. A. Kennedy,W. Zhang, and T. D. Abhayapala, "Spherical harmonic analysis and model-limited extrapolation on the sphere: Integral equation formulation," in Proc. Int. Conf. Signal Process. Commun. Syst., ICSPCS'2008, Gold Coast, Australia, Dec. 2008, p. 6.
12. A.Wyner and H. Landau, "Optimum waveform signal sets with amplitude and energy constraints," IEEE Trans. Inf. Theory, vol. IT-30, no. 4, pp. 615-622, Jul. 1984. (Pubitemid 14632097)
13. X. Liang, B. ChuanXing, C. XinZhao, and C. Jian, "Resolution enhancement of nearfield acoustic holography by interpolation using band-limited signal restoration method," Chinese Sci. Bull., vol. 53, no. 20, pp. 3142-3150, Oct. 2008.
14. D. Slepian, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty V- the discrete case," Bell Syst. Tech. J., vol. 57, no. 5, pp. 1371-1430, May-Jun. 1978. (Pubitemid 9391251)
15. A. Papoulis and M. Bertran, "Digital filtering and prolate functions," IEEE Trans. Circuit Theory, vol. CT-19, no. 6, pp. 674-681, Nov. 1972.
16. Y. Xu, S. Haykin, and R. J. Racine, "Multiple window time-frequency distribution and coherence of EEG using Slepian sequences and Hermite functions," IEEE Trans. Biomed. Eng., vol. 67, no. 7, pp. 861-866, Jul. 1999.
17. G. A. Prieto, R. L. Parker, D. J. Thomson, F. L. Vernon, and R. L. Graham, "Reducing the bias of multitaper spectrum estimates," Geophys. J. Int., vol. 171, pp. 1269-1281, 2007. (Pubitemid 350142196)
18. P. P. Mitra and H. Maniar, "Concentration maximization and local basis expansions (LBEX) for linear inverse problems," IEEE Trans. Biomed. Eng., vol. 53, no. 9, pp. 1775-1782, Sep. 2006. (Pubitemid 44285905)
19. G. G. Walter and X. Shen, "Sampling with prolate spheroidal wave functions," Sampling Theory in Signal and Image Process., vol. 2, no. 1, pp. 25-52, Jan. 2003.
20. G. G. Walter and X. Shen, "Wavelet based on prolate spheroidal wave functions," J. Fourier Anal. Appl., vol. 10, no. 1, pp. 1-26, 2004. (Pubitemid 38613784)
21. G. G. Walter and X. Shen, "Peroidic prolate spheroidal wavelets," J. Funct. Anal. Optimiz., vol. 26, no. 7-8, pp. 953-976, 2005.
22. X. Shen and G. G.Walter, "Construction of periodic prolate spheroidal wavelets using interpolation," Numer. Funct. Anal. Optimiz., vol. 28, no. 3-4, pp. 445-466, 2007. (Pubitemid 46676440)
23. C. J. Bouwkamp, "On spheroidal wave functions of order zero," J. Math. Phys., vol. 26, pp. 79-92, 1947.
24. F. A. Grunbaum, "Eigenvectors of a Toeplitz matrix: Discrete version of the prolate spheroidal wave functions," SIAM J. Alg. Disc. Meth., vol. 2, no. 2, pp. 136-141, Jun. 1981.
25. H. Xiao, V. Rokhlin, and N. Yarvin, "Prolate spheroidal wavefunctions, quadrature and interpolation," Inverse Problems, vol. 17, no. 4, pp. 805-838, 2001. (Pubitemid 32819347)
26. G. Beylkin and L. Monzon, "On generalized Gaussian quadratures for exponentials and their applications," Appl. Comp. Harm. Anal., vol. 12, no. 3, pp. 332-373, 2002.
27. E. A. Fain and M. K. Varanasi, "Minimum bandwidth basis functions for the fourth-moment bandwidth measure," in Proc. IEEE Int. Symp. Inf. Theory, Sorrento, Italy, Jun. 2000, p. 416. (Pubitemid 32393807)
28. L. E. Franks, Signal Theory. Englewood Cliffs, NJ: Prentice-Hall, 1969.
29. L. Wei, R. A. Kennedy, and T. A. Lamahewa, "Band-limited signal concentration in time-frequency," in Proc. Int. Conf. Signal Process. Commun. Syst. ICSPCS'2009, Omaha, NE, Sep. 28-30, 2009, pp. 6-0.
30. H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty-III: The dimension of the space of essentially time- and band-limited signals," Bell Syst. Tech. J, vol. 41, pp. 1295-1336, July 1962.
31. R. A. Kennedy and T. D. Abhayapala, "Spatial concentration of wavefields: Towards spatial information content in arbitrary multipath scattering," in Proc. 4th Austral. Commun. Theory Workshop, AusCTW- 2003, Melbourne, Australia, Feb. 2003, pp. 38-45.
32. L. Debnath and P. Mikusinski, Introduction to Hilbert SpacesWith Applications. San Diego, CA: Academic, 1990.