Truncation Error Estimate on Random Signals by Local Average
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Reconstruction algorithm of signals from special samples in spline spaces
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Error estimate on non-bandlimited random signals by local averages
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Signal denoising with average sampling
Digital Signal Processing
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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