A problem of continuing interest in control is the specification of sampling period that results in a system response with specified time domain characterestics such as minimum phase behaviour, overshoot and settling time. This paper presents a closed form solution for the numerator polynomial of sampled data systems. The coefficients of the numerator polynomial are given in terms of the residues and poles of the continuous time system, and the sampling period. A'so, numerical algorithm is proposed for determining reasonable sampling period for minimum phase behaviour.