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Closed-Form Mixed Design of High-Accuracy All-Pass Variable Fractional-Delay Digital Filters
Abstract
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 parameterp). 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 rangep∈ [pMin,pMax] of the VFD parameterp, 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.
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- deng, 2005, High-resolution image interpolation using two-dimensional Lagrange-type variable fractional-delay filter, Proc Int Symp Nonlinear Theory and its Applications, 214
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A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters
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Metadata
- Authors
- Deng, T.-B.
- Affiliations
- Toho University (JP)
- Corresponding author
- Deng, Tian-Bo
- ORCID
- Deng, Tian-Bo
- Venue
- IEEE Transactions on Circuits and Systems I: Regular Papers
- Published
- 2011-05
- Volume
- 58
- Issue
- 5
- Pages
- 1008-1019
- ISSN
- 1549-8328 (ISSN-L)
- 1558-0806
- OpenAlex
- W2123265291
- Cited by
- 49
- References
- 34
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 1 · 2023: 5 · 2019: 2 · 2018: 1 · 2017: 1 · 2016: 3 · 2015: 3 · 2014: 8 · 2013: 10 · 2012: 7
- FWCI
- 9.68
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Circuits and Systems I Regular Papers (publishedVersion)
- Funders
- Japan Society for the Promotion of Science (21560415)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Computer Science › Signal Processing › Advanced Adaptive Filtering Techniques
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Analog and Mixed-Signal Circuit Design
- Keywords
- all-pass filter, digital filter design, closed-form design, weighted least squares, Taylor series expansion, phase error, frequency response error, dichotomous search, low-complexity filters
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