In order to meet the requirements of the terahertz wireless communication system for large-capacity baseband signal processing algorithms, basing on the traditional filter parallel implementation algorithm derived directly from polynomial decomposition, a parallel implementation of a fast Finite Impulse Response(FIR) filter with less complexity is derived by matrix variation. On this basis, the 2 parallel, 4 parallel and 8 parallel conversion formulas and implementation architecture are given by the tensor product representation. The general implementation formula of the parallel fast FIR filter is derived and the complexity difference before and after optimization is compared. Finally, the derivation formula and specific implementation architecture of the 64 parallel fast FIR filter are given, as well as the hardware complexity comparison before and after optimization.