An Improved All-Pass Filter Design Using Closed-Form Toeplitz-plus-Hankel Matrix

Authors

  • Yue-Dar Jou R. O. C. Military Academy
  • Fu-Kun Chen Southern Taiwan University of Science and Technology

Keywords:

All-pass filter, Closed-form, Infinite Impulse Response, Least-squares, Toeplitz-plus-Hankel.

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.

Author Biographies

Yue-Dar Jou, R. O. C. Military Academy

Electrical Engineering

Fu-Kun Chen, Southern Taiwan University of Science and Technology

Computer Science and Information Engineering

Downloads

Published

2014-12-25

Issue

Vol. 1 No. 1 (2014)

Section

Articles

License

Policy for Journals/Articles with Open Access

Authors who publish with this journal agree to the following terms:
    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  1. Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work

Policy for Journals / Manuscript with Paid Access

Authors who publish with this journal agree to the following terms:
    1. Publisher retain copyright .

  1. Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work .