The FD-TD method with FFT is applied to calculate the eigenfrequencies and eige nfield distribution of a resonant cavity which is an appropriately shorted periodic slow wave circuit of N periods at both ends, the synthetic technique based on the intrinsic characteristics of spatially periodic structure is used to derive the complete dispersion relation using a few specially measured resonances. The novel method was sucessfully applied to analyze the high frequency characteristics of the coaxial relativistic backward oscillator and is applicable to slow wave structures of arbitrary geometry.