Name
Title | ||
|---|---|---|
Fast Reconstruction Methods for Bandlimited Functions from Periodic Nonuniform Sampling |
Abstract | ||
|---|---|---|
A well-known generalization of Shannon's sampling theorem states that a bandlimited function can be reconstructed from its periodic nonuniformly spaced samples if the effective sampling rate is at least the Nyquist rate. Analogous to Shannon's sampling theorem this generalization requires that an infinite number of samples be available, which, however, is never the case in practice. Most existing reconstruction methods for periodic nonuniform sampling yield very low order (often not even first order) accuracy when only a finite number of samples is given. In this paper we propose a fast, numerically robust, root-exponential accurate reconstruction method. The efficiency and accuracy of the algorithm is obtained by fully exploiting the sampling structure and utilizing localized Fourier analysis. We discuss applications in analog-to-digital conversion where nonuniform periodic sampling arises in various situations. Finally, we demonstrate the performance of our algorithm by numerical examples. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/040609586 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
sampling theorem state,periodic nonuniform sampling,analog- to-digital conversion,sampling theorem,existing reconstruction method,nonuniform periodic sampling,sampling structure,periodic nonuniform,effective sampling rate,nyquist rate,finite number,uniform interleaved sampling,shannon's sampling theorem,fast reconstruction methods,periodic nonuniformly spaced sample,oversampling,bandlimited functions,gevrey regularity,first order,nonuniform sampling,fourier analysis | Slice sampling,Periodic function,Mathematical optimization,Oversampling,Mathematical analysis,Coherent sampling,Sampling (statistics),Nyquist–Shannon sampling theorem,Nyquist rate,Mathematics,Nonuniform sampling | Journal |
Volume | Issue | ISSN |
44 | 3 | 0036-1429 |
Citations | PageRank | References |
15 | 1.13 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thomas Strohmer | 1 | 1861 | 122.72 |
| Jared Tanner | 2 | 525 | 42.48 |