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We propose a spin selector based on periodic diluted-magnetic-semiconductor/nonmagnetic-barrier (DMS/NB) superlattices subjected to an external magnetic field. We find that the periodic DMS/NB superlattices can achieve 100% spin filtering over a dramatically broader range of incident energies than the diluted-magnetic-semiconductor/semiconductor (DMS/S) case studied previously. And the positions and widths of spin-filtering bands can be manipulated effectively by adjusting the geometric parameters of the system or the strength of external magnetic field. Such a compelling filtering feature stems from the introduction of nonmagnetic barrier and the spin-dependent giant Zeeman effect induced by the external magnetic field. We also find that the external electric field can exert a significant influence on the spin-polarized transport through the DMS/NB superlattices.