Least-squares design of IIR all-pass filters using closed-form Toeplitz-plus-Hankel matrix

Least-squares design of infinite impulse response all-pass filters can be simplified by solving a system of linear equations. The set of linear equations associated matrix is further formulated as a Toeplitz-plus-Hankel form such that an efficient and robust Cholesky decomposition or Levinson technique can solve the all-pass filter coefficients. This paper proposes closed-form expressions for the computation of Toeplitz-plus-Hankel matrix. The elements of the closed-form expressions can be directly derived as the passband edges are specified without performing the sum of a series of Toeplitz-plus-Hankel matrix. Simulation results indicate that the proposed method achieves excellent performance with computational efficiency.