TY - GEN
T1 - Upper bounds on aliasing error energy for multidimensional sampling of nonbandlimited signals
AU - Sharif, Behzad
AU - Bresler, Yoram
PY - 2008/9/16
Y1 - 2008/9/16
N2 - We present upper bounds on the 2-norm of the aliasing error in multidimensional Shannon sampling. Our bounds complement the previously known 1-norm upper bounds for the peak aliasing error. The proposed bounds provide a good estimate of the total error energy for any signal, rather than just for certain pathological extremals, as is the case with the 1-norm bounds which, as a result, tend to be too conservative for practical applications. The sampling representation is general, possibly multiband, and not restricted to bandlimited signals. Error bounds are phrased in terms of the energy of signal components that lie outside the assumed band-region. Therefore, they are easy to interpret and compute as is demonstrated for two practical signal classes, namely signals with exponential or polynomial out-of-band decay.
AB - We present upper bounds on the 2-norm of the aliasing error in multidimensional Shannon sampling. Our bounds complement the previously known 1-norm upper bounds for the peak aliasing error. The proposed bounds provide a good estimate of the total error energy for any signal, rather than just for certain pathological extremals, as is the case with the 1-norm bounds which, as a result, tend to be too conservative for practical applications. The sampling representation is general, possibly multiband, and not restricted to bandlimited signals. Error bounds are phrased in terms of the energy of signal components that lie outside the assumed band-region. Therefore, they are easy to interpret and compute as is demonstrated for two practical signal classes, namely signals with exponential or polynomial out-of-band decay.
KW - Aliasing error
KW - Error energy
KW - Multidimensional
KW - Nonbandlimited
KW - Shannon sampling
UR - http://www.scopus.com/inward/record.url?scp=51449104132&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=51449104132&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2008.4518460
DO - 10.1109/ICASSP.2008.4518460
M3 - Conference contribution
AN - SCOPUS:51449104132
SN - 1424414849
SN - 9781424414840
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3717
EP - 3720
BT - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
T2 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Y2 - 31 March 2008 through 4 April 2008
ER -