Fast real-time convolution algorithm for microwave multiport networks with nonlinear terminations

This work presents an efficient convolution algorithm for frequency domain data in the presence of nonlinear terminations. By combining the conventional convolution and fast Fourier transform technique, the cost for real-time convolution is reduced from O(N²) to O(Nlog²N). This algorithm can be easily incorporated into multiple-input-multiple-out linear circuit systems with descriptions by impedance, admittance, or scattering matrix which is measured or precomputed in the frequency domain. Optimal number of points for conventional convolution in this algorithm can also be theoretically determined to give the best computational efficiency. A nonlinearly terminated eight-port circuit, characterized by scattering matrix, with multiple excitations is employed to demonstrate the efficiency of this algorithm.