Dyadic Calculus and Sampling Theorems for Functions with Multidimensional Domain. II: Applications to Dyadic Sampling Representations

Part II is concerned with applications of the general theory of multidimensional dyadic analysis to dyadic sampling theorems for various types of signals together with rates of approximation and orders of magnitude for the aliasing error, respectively. The theory developed in Part I—the contents of which are assumed to be known here—is now applied in order to study various types of sampling theorems. It may be mentioned that there does not exist any paper at all dealing with multidimensional dyadic sampling theorems. This can, for example, be seen in the survey paper by A. J. Jerri (1977, Proc. Inst. Electr. Engrs. 65, 1565–1596) . Nevertheless, in the classical multidimensional Fourier case there are some papers dealing with sampling representations for functions of several variables (see, e.g., Prosser (1966) , Petersen and Middleton (1962) , and Miyakawa (1959) ).