Approximating band- and energy-limited signals in the presence of jitter. (English) Zbl 0917.65119
This paper deals with the recovering of band- and energy-limited functions \(f\) from noisy samples taken at slightly wrong sampling points \(t_k\) \((k= 1,\dots, n)\). With other words, the information about \(f\) consists of finitely many values \(f(t_k+ \gamma_k)+ \delta_k\) \((k= 1,\dots, n)\), where \(|\gamma_k|\leq\gamma\) and \(\|(\delta_k)^n_{k= 1}\|\leq\delta\). This inaccuracy in reading the sampling points is called jitter.
The aim of this paper is to analyze how the minimal worst-case recovery error depends on \(\gamma\) and \(\delta\). This is accomplished by proving tight upper and lower bounds for the diameter of information. The main result implies that the jitter causes an error of order \(\gamma\Omega^{3/2}+ \delta\), where \(\Omega\) denotes the bandwidth of \(f\).
The aim of this paper is to analyze how the minimal worst-case recovery error depends on \(\gamma\) and \(\delta\). This is accomplished by proving tight upper and lower bounds for the diameter of information. The main result implies that the jitter causes an error of order \(\gamma\Omega^{3/2}+ \delta\), where \(\Omega\) denotes the bandwidth of \(f\).
Reviewer: M.Tasche (Rostock)
MSC:
| 65T40 | Numerical methods for trigonometric approximation and interpolation |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 42A10 | Trigonometric approximation |
Keywords:
band-limited function; recovering; jitter; diameter of information; approximation of band-limited signal; energy-limited function; minimal worst-case recovery errorReferences:
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