Title :
On the necessity of Papoulis´ result for multidimensional GSE
Author_Institution :
Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa, Israel
fDate :
4/1/2004 12:00:00 AM
Abstract :
Papoulis´ generalized sampling expansion (GSE) can be carried out if a set of linear equations has a solution. This enables the reconstruction of a signal from its filtered and downsampled versions. We show that the existence of this solution is also a necessary condition for the reconstruction of the signal from the available data. Special attention is given to the case of recurrent multidimensional sampling.
Keywords :
matrix algebra; multidimensional signal processing; signal reconstruction; signal sampling; Papoulis´ generalized sampling expansion; linear equations; matrix; multidimensional generalized sampling expansion; recurrent multidimensional sampling; signal reconstruction; Equations; Filters; Fourier transforms; Frequency; Lattices; Multidimensional systems; Nonuniform sampling; Sampling methods; Signal reconstruction; Sufficient conditions;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2004.824022
