TY - GEN
T1 - Concentration uncertainty principles for signals on the unit sphere
AU - Khalid, Zubair
AU - Durrani, Salman
AU - Sadeghi, Parastoo
AU - Kennedy, Rodney A.
PY - 2012
Y1 - 2012
N2 - The uncertainty principle is an important and powerful tool, with many applications in signal processing. This paper presents two concentration uncertainty principles for signals on the sphere which relate the localization of the concentration of a signal in spatial and spectral domains, as an analogue of the general Donoho and Stark uncertainty principles in time-frequency analysis. Using the spherical and spectral truncation operators, we derive the L 1-norm and L 2-norm uncertainty principles which respectively relate the signal concentration in spatial and spectral domains as absolute value and the energy of a signal. We also analyze the sharpness of the bound imposed by the derived L 2-norm uncertainty principle. The proposed uncertainty measures can be applied to signal processing problems on the sphere.
AB - The uncertainty principle is an important and powerful tool, with many applications in signal processing. This paper presents two concentration uncertainty principles for signals on the sphere which relate the localization of the concentration of a signal in spatial and spectral domains, as an analogue of the general Donoho and Stark uncertainty principles in time-frequency analysis. Using the spherical and spectral truncation operators, we derive the L 1-norm and L 2-norm uncertainty principles which respectively relate the signal concentration in spatial and spectral domains as absolute value and the energy of a signal. We also analyze the sharpness of the bound imposed by the derived L 2-norm uncertainty principle. The proposed uncertainty measures can be applied to signal processing problems on the sphere.
KW - Slepian concentration problem
KW - bandlimited signals
KW - signal extrapolation
KW - uncertainty principle
KW - unit sphere
UR - http://www.scopus.com/inward/record.url?scp=84867593678&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2012.6288724
DO - 10.1109/ICASSP.2012.6288724
M3 - Conference contribution
SN - 9781467300469
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3717
EP - 3720
BT - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings
T2 - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
Y2 - 25 March 2012 through 30 March 2012
ER -