The simple repetitive control system proposed by Yamada et al. is a type of servomechanism for periodic reference inputs. This system follows a periodic reference input with a small steady-state error, even if there is periodic disturbance or uncertainty in the plant. In addition, simple repetitive control systems ensure that transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, Yamada et al. proposed the parameterization of all stabilizing two-degrees-of-freedom (TDOF) simple repetitive controllers that can specify the input-output characteristic and the disturbance attenuation characteristic separately. However, when using the method of Yamada et al., it is complex to specify the low-pass filter in the internal model for the periodic reference input that specifies the frequency characteristics. This paper extends the results of Yamada et al. and proposes the parameterization of all stabilizing TDOF simple repetitive controllers with specified frequency characteristics in which the low-pass filter can be specified beforehand.