Periodic structures have renewed applications in microwave engineering, especially with the advent of unusual artificial materials such as EBG structures and metamaterials. In this work, it is shown that spatial modulation of periodic structures provides a multiband behavior that depends on the amplitude or position modulation function. The number of stop bands, band-widths, center frequencies depends on the modulation function and type. The effect of the modulation function selection, as well as the effect of increasing the number of modulated loads within the period on the band diagram in both Load Amplitude Modulation and Load Position Modulation cases is studied. The concept of spatial modulation is applied to Left Hand-Right Hand rectangular waveguides with dielectric filled corrugations, and is proved to create new LH bands. Also, applications to microwave filter design by selecting the suitable terminating impedance based on the Bloch impedance calculations, to provide better filtering response, is discussed. The concept of periodic spatial modulation is a step towards the optimal design of the unit cell to engineer the band diagram of the periodic structure.