A Theoretical Question in the Optimal Design of Matrix Decomposition Based FIR Filter

The matrix decomposition (MD) based finite impulse response (FIR) filter is a low-complexity FIR filter. It has been tested the coefficients of the MD-FIR filter can be effectively optimized by the trust-region-iterative-gradient-searching (TR-IGS) algorithm. This algorithm solves the convex-approximation-problem of the original coefficients optimization problem. In this study, we deal with the relationship between the theoretical termination point of the TR-IGS and the optimal solution of the original coefficients optimization problem.