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Reconstruction of band-limited signals from local averages

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2 Author(s)
Wenchang Sun ; Morningside Center of Math., Acad. Sinica, Beijing, China ; Xingwei Zhou

The sampling theorem says that every band-limited signal is uniquely determined by its sampled values provided the sampling points satisfy certain conditions. However, sampled values obtained in practice may not be the exact values of a signal at sampling points, but only averages of the signal near these points. Grochenig (1992) proved that band-limited signals can be reconstructed exactly from local averages if the sampling density is large enough. We study the reconstruction of band-limited signals from local averages with symmetric averaging functions. We study the aliasing error arising when a non-band-limited signal is reconstructed from local averages and give explicit error bounds. Since the classical "point sampling" can be viewed as a limiting case of average sampling, we indeed give new aliasing error bounds for both regular and irregular sampling

Published in:

IEEE Transactions on Information Theory  (Volume:48 ,  Issue: 11 )