An efficient least-squares design of IIR all-pass filter

Least-squares design of digital filters is generally achieved by solving a system of linear equations. The matrices involved in the set of linear equations can be formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided with effectiveness. In this paper, some trigonometric properties are further exploited to obtain the closed-form expressions required for the system associated matrices in the least-squares design of IIR all-pass filters. Simulation results confirm that the proposed method achieves efficiency and good performance.