New Formulas for Irregular Sampling of Two-Bands Signals

References

[1] H. J. Landau, “Sampling, Data Transmission, and the Nyquist Rate,” Proceedings of the IEEE, Vol. 55, No. 10, 1967, pp. 1701-1706. doi:10.1109/PROC.1967.5962

[2] B. Lacaze, “About Bi-Periodic Samplings,” Sampling Theory in Signal and Image Processing, Vol. 8, No. 3, 2009, pp. 287-306.

[3] B. Lacaze, “Equivalent Circuits for the PNS2 Sampling Scheme,” IEEE Circuits and Systems, Vol. 57, No. 11, 2010, pp. 2904-2914. doi:10.1109/TCSI.2010.2050228

[4] A. J. Jerri, “The Shannon Sampling Theorem. Its Various Extensions and Applications. A Tutorial Review,” Proceedings of the IEEE, Vol. 65, No. 11, 1977, pp. 1565-1596. doi:10.1109/PROC.1977.10771

[5] B. Lacaze, “Reconstruction Formula for Irregular Sampling,” Sampling Theory in Signal and Image Processing, Vol. 4, No. 1, 2005, pp. 33-43.

[6] B. Lacaze, “The Ghost Sampling Sequence Method,” Sampling Theory in Signal and Image Processing, Vol. 8, No. 1, 2009, pp. 13-21.

[7] H. Cramer and M. R. Leadbetter, “Stationary and Related Stochastic Processes,” Wiley, New York, 1966.

[8] A. Papoulis, “Signal Analysis,” McGraw Hill, New York, 1977.

[9] J. R. Higgins, “A Sampling Theorem for Irregular Sample Points,” IEEE Transactions on Information Theory, Vol. 22, No. 5, 1976, pp. 621-622.
doi:10.1109/TIT.1976.1055596

[10] J. R. Higgins, “Some Gap Sampling Series for Multiband Signals,” Signal Processing, Vol. 12, No. 3, 1987, pp. 313-319. doi:10.1016/0165-1684(87)90100-9

[11] J. L. Yen, “On Nonuniform Sampling of Bandwidth-Limited Signals,” IRE Transactions on Circuit Theory, Vol. 3, No. 4, 1956, pp. 251-257.

[12] B. Lacaze, “About a Multiperiodic Sampling Scheme,” IEEE Signal Processing Letters, Vol. 6, No. 12, 1999, pp. 307-308. doi:10.1109/97.803430

[13] B. Lacaze, “A Theoretical Exposition of Stationary Processes Sampling,” Sampling Theory in Signal and Image Processing, Vol. 4, No. 3, 2005, pp. 201-230.

[14] K. Seip, “An Irregular Sampling Theorem for Functions Bandlimited in a Generalized Sense,” SIAM Journal on Applied Mathematics, Vol. 47, No. 5, 1987, pp. 1112-1116. doi:10.1137/0147073

[15] A. I. Zayed and P. L. Butzer, “Lagrange Interpolation and Sampling Theorems,” In: F. Marvasti, Ed., Nonuniform Sampling: Theory and Practice, Kluwer Academic, 2001, pp. 123-168. doi:10.1007/978-1-4615-1229-5_3

[16] Y.-P. Lin and P. P. Vaidyanathan, “Periodically Nonuniform Sampling of Bandpass Signals,” IEEE Transactions on Circuits and Systems II, Vol. 45, No. 3, 1998, pp. 340-351.

[17] R. Venkataramani, “Perfect Reconstruction Formulas and Bounds on Aliasing Error in Sub-Nyquist Nonuniform Sampling of Multibands Signals,” IEEE Transactions on Information Theory, Vol. 46, No. 6, 2000, pp. 2173-2183.