Average sampling in shift invariant subspaces with symmetric averaging functions. (English) Zbl 1029.94009
Summary: We study the reconstruction of functions in shift invariant subspaces from local averages with symmetric averaging functions. We present an average sampling theorem for shift invariant subspaces and give quantitative results on the aliasing error and the truncation error. We show that every square integrable function can be approximated by its average sampling series. As special cases we also obtain new error bounds for regular sampling. Examples are given.
MSC:
| 94C10 | Switching theory, application of Boolean algebra; Boolean functions (MSC2010) |
| 40A30 | Convergence and divergence of series and sequences of functions |
| 41A30 | Approximation by other special function classes |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
Keywords:
Average sampling; Sampling theorems; Shift invariant subspaces; Aliasing error; Truncation errorReferences:
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