Modulation noise in the reproducing process of a VTR may influence the error rate. We had already proposed a model of modulation noise which can be applied to sine wave recording. In this paper we study a mathematical model of modulation noise in reproduced digital signals. We analyzed the total noise by subtracting the ensemble mean from the reproduced signal. Based on this analysis, we confirmed that the formula for reproduced signal including modulation noise can be applied to digital signals. In addition, we found that modulation noise is dominant in the signal bandwidth.