Inspired by pulse-pair generation with periodic phase jump, the generation of dispersed pulses with aperiodic binary spectral phase jump (ABSPJ) is proposed and theoretically investigated. It is presented by the numerical simulations that two dispersed pulses can be generated by ABSPJ of π. The dispersion of one pulse is opposite to the other and can be tuned freely with engineering of the phase jump. The generated dispersed pulse-pair is potentially of great interest for various applications, such as two-dimensional spectroscopy, double pulses laser-wakefield acceleration (LWFA) and chirp management in dual-chirped optical parametric amplification (DC-OPA) system to generate TW single-cycle mid-infrared (MIR) pulses. Furthermore, a pulse shaper configured as a micro-electro-mechanical systems (MEMS) located at the Fourier plane of a 4-f dispersion-free compressor is suggested and the implementation in a high repetition optical parametric chirped pulse amplification (OPCPA) system with picosecond pump has been numerically studied. The simulations showed that MEMS of 900 pixels is enough to pre-compensate TOD of 200000 fs3 for a pulse of 20 fs. Because pixel with only two piston-levels is necessary for such MEMS, the pulse shaper is expected to be compact and reliable.