In this paper, we address identification of a class of multi-input single-output (MISO) linear time-invariant (LTI) discrete-time systems, where the MISO system is composed of several single-input single-output (SISO) LTI systems and only the sum of the output of each SISO system can be measured. By exciting one SISO system and employing periodic inputs to the remaining SISO systems, we decompose the MISO system into the excited SISO system where its input and output can be calculated from the measured data. As such, the original parameters for each SISO system can be estimated using the well-established identification techniques. The proposed method using periodic inputs is also extended to identification beyond the Nyquist frequency. Both simulation and experimental results on identification of actuators in the dual-stage hard disk drive are carried out to demonstrate the efficacy of the proposed approach.