Sampling approximation of continuous functions with multidimensional domain (Corresp.)
Wolfgang Splettstößer · IEEE Transactions on Information Theory · 1982
After evaluating Shannon's sampling theorem for functions of several variables, the aliasing error is estimated in dependence upon smoothness conditions. As a main tool the concept of multidimensional convolution integrals is introduced, in particular those of de La Vallée Poussin, which are also helpful in constructing generalized sampling series having better aliasing bounds.