Abstract. We analyzed asymptotic solutions to fuzzy cellular automata of first order in time with 2 or 3 neighbors in space. The asymptotic solution is a solution evolved after enough time steps from initial value. We proved solutions become uniform or stable asymptotically focusing on one of the following properties; (i) There exist a montonicity on every site. (ii) Lyapunov function exists. (iii) The maximum or minimum values changes monotonicity.

Abstract. For Fourier transform with a limited frequency domain, an approximation formula using continuous Euler transform has been devised by Ooura, and its error analysis has been done by Tanaka. In this paper, we construct an approximation formula for Fourier transform in the whole frequency domain for an exponentially decreasing function by combining Sinc method, which is one of function approximation methods, and Ooura’s formula, perform error analysis and confirm its correctness by numerical experiments. As an extension, we also devise a method to achieve the given approximation error.