TY - JOUR
T1 - Perfect reconstruction formulas and bounds on aliasing error in sub-Nyquist nonuniform sampling of multiband signals
AU - Venkataramani, Raman
AU - Bresler, Yoram
N1 - Funding Information:
Manuscript received July 12, 1998; revised March 8, 2000. This work was supported in part by the Joint Services Electronic Program under Grant N00014-96-1-0129, the National Science Foundation under Grant MIP 97-07633, and DARPA under Contract F49620-98-1-0498.
PY - 2000/9
Y1 - 2000/9
N2 - We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class B(F) of multiband signals with spectral support F, at rates arbitrarily close to the Landau minimum rate equal to the Lebesgue measure of F, even when F does not tile R under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band-limited to the `span of F' (the smallest interval containing F) which is a bigger class than the valid signals B(F), band-limited to F. We also examine the performance of the reconstruction system when the input contains additive sample noise.
AB - We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class B(F) of multiband signals with spectral support F, at rates arbitrarily close to the Landau minimum rate equal to the Lebesgue measure of F, even when F does not tile R under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band-limited to the `span of F' (the smallest interval containing F) which is a bigger class than the valid signals B(F), band-limited to F. We also examine the performance of the reconstruction system when the input contains additive sample noise.
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U2 - 10.1109/18.868487
DO - 10.1109/18.868487
M3 - Article
AN - SCOPUS:0034270365
SN - 0018-9448
VL - 46
SP - 2173
EP - 2183
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
ER -