We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace sat...<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.展开更多
基金This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Educationthe Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
文摘We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
文摘<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
