Error estimates for sampling sums based on convolution integrals
The classical Shannon sampling theorem is concerned with the representation of bandlimited signal functions by a sum built up from a countable number of samples. It is shown that a not necessarily bandlimited function f can be approximately represented by generalized sampling sums which originate fr...
Saved in:
| Published in | Information and control Vol. 45; no. 1; pp. 37 - 47 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.01.1980
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | The classical Shannon sampling theorem is concerned with the representation of bandlimited signal functions by a sum built up from a countable number of samples. It is shown that a not necessarily bandlimited function
f can be approximately represented by generalized sampling sums which originate from discretized convolution integrals known, e.g., in approximation theory. The rate of convergence of the new sums to
f is precisely as good as that of the associated convolution integrals. This gives sufficient as well as matching necessary conditions for a certain rate of convergence. |
|---|---|
| ISSN: | 0019-9958 1878-2981 |
| DOI: | 10.1016/S0019-9958(80)90857-8 |