Journal of Computer Science Technology Updates  (Volume 1 Issue 1)

 An Improved All-Pass Filter Design Using Closed-Form Toeplitz-plus-Hankel Matrix Jcstu
Pages 19-25

Yue-Dar Jou and Fu-Kun Chen

DOI: http://dx.doi.org/10.15379/2410-2938.2014.01.01.03
Published: 24 December 2014
Abstract
The least-squares design of infinite impulse response all-pass filter can be formulated as to solve a system of linear equations without directly computing a matrix inversion. The set of linear equations associated matrix is further expressed as a Toeplitz-plus-Hankel matrix such that the optimal filter coefficients are efficiently solved by employing a robust Cholesky decomposition or the split Levinson technique. This paper proposes closed-form expressions for efficiently computing Toeplitz-plus-Hankel matrix based on trigonometric identities. The closed-form expressions of the Toeplitz-plus-Hankel matrix can be directly evaluated as the passband edges are specified without sampling the frequency band as that of the previous computing-efficiency algorithm. The proposed new and simpler closed-form expressions are indicated from simulation results to accurately improve the design performance as well as achieve computational efficiency.
Keywords
 All-pass filter, Closed-form, Infinite Impulse Response, Least-squares, Toeplitz-plus-Hankel.
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