An algorithm for linear discretized filtering and its dual discretized quadratic-coat optimal control for real-time applications on continuous-time systems is presented. The algorithm is optimal in the sense of achieving the optimal approximation, by discretized time processing, to the ideal but non-realizable continuous-time processing. It provides the possibility to choose the sampling rate beforehand by obtaining the corresponding error-variance or the policy cost. The problem's horizon can be finite. Properties and applications of the algorithm are explored. The concept of duality is made apparent and given-new insight.