We present a method of using one-dimensional dielectric multilayer structures for designing terahertz frequency spreading filters. The interference of terahertz pulses in these structures composed of alternating weak and strong refractive materials allows design of well-separated THz frequency components within a modulation-limited THz spectral envelope. The design characteristics of these coarse THz combs are limited by the saturation effect and also by the deformation of the THz pulse time-traveling within the structure. The details of the designed THz waveform synthesis from these THz multilayer spectral filters are verified by experiments using time-domain terahertz pulsed spectroscopy.