Recovery of Missing Samples in Multi-channel Oversampling of Multi-banded Signals
We show that in a two-channel sampling series expansion
of band-pass signals, any finitely many missing samples can
always be recovered via oversampling in a larger band-pass region.
We also obtain an analogous result for multi-channel oversampling
of harmonic signals.
[1] M.G. Beaty, M.M. Dodson, The distribution of sampling rates for signals
with equally wide, equally spaced spectral bands, SIAM J. Appl. Math,
vol. 53, no. 3, 1993, 893-906.
[2] P.J.S.G. Ferreira, Incomplete sampling series and the recovery of missing
samples from oversampled band-limited signals, IEEE Trans. Signal
Processing, vol. 40, no. 1, 1992, 225-227.
[3] P.J.S.G. Ferreira, The stability of a procedure for the recovery of lost
samples in band-limited signals, Signal Proc., vol. 40, no. 3, 1994, 195-
205.
[4] J.R. Higgins, Sampling Theory in Fourier and Signal Analysis, Oxford
University Press, Oxford, 1996.
[5] Y.M. Hong, J.M. Kim and K.H. Kwon, Sampling theory in abstract
reproducing kernel Hilbert space, submitted.
[6] J.M. Kim and K.H. Kwon, Recovery of finite missing samples in twochannel
oversampling, preprint.
[7] J.M. Kim, K.H. Kwon and E.H. Lee, Asymmetric multi-channel sampling
formula and its aliasing error, submitted.
[8] R.J. Marks II, Introduction to Shannon Sampling and Interpolation
Theory, Springer-Verlag, New York, 1991.
[9] A. Papoulis, Generalized sampling expansion, IEEE Trans. on circuits
and systems, vol. 24, no. 11, 1977, 652-654.
[10] D.M.S. Santos and P.J.S.G Ferreira, Reconstruction from missing function
and derivative samples and oversampled filter banks, in Proceedings
of the IEEE International Conference on Acoustics, Speech, and Signal
Processing, ICASSP 04, vol. 3, 2004, 941-944.
[1] M.G. Beaty, M.M. Dodson, The distribution of sampling rates for signals
with equally wide, equally spaced spectral bands, SIAM J. Appl. Math,
vol. 53, no. 3, 1993, 893-906.
[2] P.J.S.G. Ferreira, Incomplete sampling series and the recovery of missing
samples from oversampled band-limited signals, IEEE Trans. Signal
Processing, vol. 40, no. 1, 1992, 225-227.
[3] P.J.S.G. Ferreira, The stability of a procedure for the recovery of lost
samples in band-limited signals, Signal Proc., vol. 40, no. 3, 1994, 195-
205.
[4] J.R. Higgins, Sampling Theory in Fourier and Signal Analysis, Oxford
University Press, Oxford, 1996.
[5] Y.M. Hong, J.M. Kim and K.H. Kwon, Sampling theory in abstract
reproducing kernel Hilbert space, submitted.
[6] J.M. Kim and K.H. Kwon, Recovery of finite missing samples in twochannel
oversampling, preprint.
[7] J.M. Kim, K.H. Kwon and E.H. Lee, Asymmetric multi-channel sampling
formula and its aliasing error, submitted.
[8] R.J. Marks II, Introduction to Shannon Sampling and Interpolation
Theory, Springer-Verlag, New York, 1991.
[9] A. Papoulis, Generalized sampling expansion, IEEE Trans. on circuits
and systems, vol. 24, no. 11, 1977, 652-654.
[10] D.M.S. Santos and P.J.S.G Ferreira, Reconstruction from missing function
and derivative samples and oversampled filter banks, in Proceedings
of the IEEE International Conference on Acoustics, Speech, and Signal
Processing, ICASSP 04, vol. 3, 2004, 941-944.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64814", author = "J. M. Kim and K. H. Kwon", title = "Recovery of Missing Samples in Multi-channel Oversampling of Multi-banded Signals", abstract = "We show that in a two-channel sampling series expansion
of band-pass signals, any finitely many missing samples can
always be recovered via oversampling in a larger band-pass region.
We also obtain an analogous result for multi-channel oversampling
of harmonic signals.", keywords = "oversampling, multi-channel sampling, recovery of missing samples, band-pass signal, harmonic signal", volume = "1", number = "8", pages = "395-3", }
