Recovery of bandlimited signals using poisson samples
Abstract
The problem of interpolation of bandlimited deterministic signals using Lagrange polynomials which are based upon observations taken at Poisson instants is considered. Let the signal be bandlimited to the interval (3.14, 3.14) radians, and let the average sampling rate of the Poisson process be beta samples per second. When the Lagrange interpolation polynomials are based upon the Poisson sampling instants (t(sub k)) and the observed data s(t(sub k)), then the meansquared error converges to zero as the number of observations increases to infinity for all sampling rates beta equal to or greater than 3(3.14)/2. The rate of convergence is exponential for beta greater than 3(3.14)/2. The above results hold for center point interpolation (i.e., an equal number of samples on each side of the interpolation point). For the case of extrapolation, the sampling rate must be increased to 3(3.14).
 Publication:

Final Report Naval Ocean Systems Center
 Pub Date:
 October 1979
 Bibcode:
 1979nosc.reptR....K
 Keywords:

 Numerical Analysis;
 Signal Analysis;
 Signal Processing;
 Extrapolation;
 Fourier Transformation;
 Frequencies;
 Interpolation;
 Poisson Density Functions;
 Polynomials;
 Stochastic Processes;
 Communications and Radar