Approximation properties of multivariate Kantorovich-Kotelnikov sampling type operators generated by different band-limited functions are studied. In particular, a wide class of functions with discontinuous Fourier transform is considered. The $L_p$-rate of convergence for these operators is given in terms of the classical moduli of smoothness. Several examples of the Kantorovich-Kotelnikov operators generated by the sinc-function and its linear combinations are provided. This is joint work with Maria Skopina (St. Petersburg State University).