Abstract: In this paper we discuss the truncated error estimate on Shannon sampling theorem of bandlimited functions. We mainly focus on error of pointwise type, uniform type and integral type. In pointwise type, we use the method of calcuating Dirichlet kernel and obtain the order O(1/N); in uniform and integral type, by calculating the decaying condition imposed on the function, we can get the uniform and integral estimate.

Key words: truncated error, pointwise estimate, uniform estimate, integral estimate