We establish a general model of a finite periodic system by n pairs of alternating ferromagnetic and nonmagnetic (FNF) layers. Using Bloch spin wave quantum theory, the basic properties of alternating FNF layers and the dependence of property of electron wave scattering in alternating layers on the number of layers are investigated. It is found that an electron wavefunction in the system can be expressed as the superposition of eigenvectors of a transfer matrix or Bloch-like functions in an infinite periodic system. Form this function we can obtain an exact solution for monochromatic wave scattering of a system with an arbitrary number of layers. On this basis, the dependences of reflection and transmission coefficients on energy for the electron wavefunction in a periodic system are determined. The calculation of spectral window shows that its energy position and width are the same as those of almost full reflection region. The system can be used as spin filter due to high-energy dispersion and dependence of exchange energy on electron spin direction.