Abstract: Threshold Logic Gate (TLG) is receiving much attention because of its logic versatility and functionally complete. For the circuit design based on TLG, a method is described to determine whether a function is threshold or not with the spectral technology. The weights and threshold can be calculated by spectral coefficients. As for non-threshold function, a novel logic synthesis algorithm is proposed, which can transform non-threshold function to the sum of some threshold functions. Furthermore, any Boolean logic function can be realized by a collection of TLG using the method in this paper. Proposed algorithm provides a method for circuit design of resonant tunneling diode.