This paper presents a filter structure that allows the user to place desired poles and the necessary zeros to achieve periodic regulation to the closed-loop sensitivity through Internal Model Control framework. The periodic regulation is aimed at stable SISO linear systems suffering from input dead-time and having no closed right-half plane zeros. The negative effects of the dead time on tracking/rejection are compensated by introducing another delay which is tuned independently from the filter thanks to its structure. The main focus is given to constructing the filter with polynomials. However, it can be readily extended to quasi-polynomials. The findings are verified with a computer simulation of a vibration control task.