By Topic

Closed-Form Mixed Design of High-Accuracy All-Pass Variable Fractional-Delay Digital Filters

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Tian-Bo Deng ; Dept. of Inf. Sci., Toho Univ., Chiba, Japan

This paper presents a closed-form method for minimizing the weighted squared error of variable fractional-delay (VFD) of an all-pass VFD digital filter under an equality constraint on its normalized root-mean-squared (NRMS) error of variable frequency response (VFR). The main purpose is to reduce the squared VFD error as much as possible while keeping its NRMS VFR error exactly at a predetermined value. We first prove that the linearized VFR error of an all-pass VFD filter is almost the same as its linearized phase error, and then convert the equality-constrained weighted-least-squares (WLS) design into an unconstrained optimization problem through the minimization of a mixed error function that mixes the weighted squared VFD error and squared VFR error. To reduce the computational complexity, we derive a closed-form mixed error function by utilizing Taylor series expansions of trigonometric functions. Therefore, the error functions can be efficiently computed without discretizing the design parameters (frequency ω and VFD parameter p). The closed-form mixed error function not only reduces the computational complexity, but also speeds up the design process as well guarantees the optimality of the final solution. Furthermore, a two-point search (dichotomous search) scheme is proposed for finding the optimal range p ∈ [pMin,pMax] of the VFD parameter p, and then the subfilter orders are optimized under a given filter complexity constraint (the number of all-pass VFD filter coefficients). This two-stage optimization process utilizes the NRMS VFD error as an error criterion. Design examples and comparisons are given to demonstrate that the closed-form mixed WLS method yields low-complexity all-pass VFD filters with a high-accuracy VFD response but without noticeably degrading its frequency response.

Published in:

Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:58 ,  Issue: 5 )