The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Analytical approximations of fractional delays: Lagrange interpolators and allpass filters
Abstract
We propose in this paper a new point of view which unifies two well known filter families for approximating ideal fractional delay filters: Lagrange interpolator filters (LIF) and Thiran allpass filters. We achieve this unification by approximating the ideal Fourier transform of the fractional delay according to two different Pade approximations: series expansions and continued fraction expansions, and by proving that both approximations correspond exactly either to the LIF family or to the allpass delay filters family. This leads to an efficient modular implementation of LIFs.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The Nth-order Thiran fractional delay filter (1) is equal to the (2N+1)st approximant of (4).
“the N th-order Thiran fractional delay filter (1) is equal to the (2 N +1) st approximant of (4)”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
The method of [9] attempted to replace z^-1 with z^-1 - 1.
“the method of [9] attempted to replace z -1 with z -1 -1 .”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
Tassart and Depalle's structure is not realizable because of delay-free loops.
“their structure is not realizable because of delay-free loops.”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
The transfer function given by substitutions (7) yields the fractional part of (5).
“the transfer function given by the given substitutions yields the fractional part of (5)”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
The proposed method successfully overcomes the problem of [9].
“the proposed method successfully overcomes the problem of [9].”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
The system z^-1 - 1 included the direct feedthrough term -1 that resulted in the unrealizable ladder structure with delay-free loops.
“This system included the direct feedthrough term -1 that resulted in the unrealizable ladder structure with delay-free loops.”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
The ideal fractional delay z^-D can be expressed in terms of the infinite continued fraction as given.
“the ideal fractional delay z -D can be expressed in terms of the infinite continued fraction as given.”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
The strategy in [9] fails to provide feasible filter structures.
“this strategy fails to provide feasible filter structures.”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
The reason for this failure lies in the substitution z^-1 <- z^-1 - 1.
“The reason for this failure lies in the substitution z -1 ← z -1 -1 .”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
If we carry out this substitution on the block diagram of (6), the resultant block diagram yields delay-free loops; thus, the resultant filter structure is not realizable.
“If we carry out this substitution on the block diagram of (6), the resultant block diagram yields delay-free loops; thus, the resultant filter structure is not realizable.”
From A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters (2014) · cites this paper as [9]
Citations
Cites
(1972) · Cited by 17,806
Analytic Theory of Continued Fractions
Jones, W., Thron, W., & Waadeland, H. (1982) · Lecture notes in mathematics · doi:10.1007/bfb0093301 · Cited by 1,207
Splitting the unit delay [FIR/all pass filters design]
Laakso, T. I., Valimaki, V., Karjalainen, M., & Laine, U. K. (1996) · IEEE Signal Processing Magazine · doi:10.1109/79.482137 · Cited by 1,168
Multirate digital signal processing
(1983) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(83)90133-7 · Cited by 653
Recursive digital filters with maximally flat group delay
Thiran, J.-P. (1971) · IEEE Transactions on Circuit Theory · doi:10.1109/tct.1971.1083363 · Cited by 247
Discrete-Time Modeling of Acoustic Tubes Using Fractional Delay Filters
V�lim�ki, V. (1998) · Cited by 123
Explicity formulas for weighting coefficients of maximally flat tunable FIR delays
Hermanowicz, E. (1992) · Electronics Letters · doi:10.1049/el:19921239 · Cited by 93
Fractional Delays using Lagrange Interpolators
Tassart, S., & Depalle, P. (1996) · HAL (Le Centre pour la Communication Scientifique Directe) · Cited by 2
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Fractional Delay Filter Design Based on Truncated Lagrange Interpolation
Valimaki, V., & Haghparast, A. (2007) · IEEE Signal Processing Letters · doi:10.1109/lsp.2007.898856 · Cited by 66
Results on Maximally Flat Fractional-Delay Systems
Samadi, S., Ahmad, M. O., & Swamy, M. N. S. (2004) · IEEE Transactions on Circuits and Systems I: Regular Papers · doi:10.1109/tcsi.2004.836848 · Cited by 51
Fractional Delay Filters—Design and Applications
Välimäki, V., & Laakso, T. I. (2001) · Information Technology: Transmission, Processing, and Storage · doi:10.1007/978-1-4615-1229-5_20 · Cited by 32
Closed-Form Design of Half-Sample Delay IIR Filter Using Continued Fraction Expansion
Tseng, C.-C. (2007) · IEEE Transactions on Circuits and Systems I: Regular Papers · doi:10.1109/tcsi.2006.887643 · Cited by 9
A Simple Ladder Realization of Maximally Flat Allpass Fractional Delay Filters
Koshita, S., Abe, M., & Kawamata, M. (2014) · IEEE Transactions on Circuits and Systems II: Express Briefs · doi:10.1109/tcsii.2013.2296131 · Cited by 5
Metadata
- Authors
- Tassart, S., & Depalle, P.
- ORCID
- Depalle, P.
- Venue
- 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing
- Publisher
- IEEE Comput. Soc. Press
- Published
- 2002-11-22
- Volume
- 1
- Pages
- 455-458
- ISSN
- 1520-6149 (ISSN-L)
- OpenAlex
- W2160023860
- Cited by
- 27
- References
- 8
- Citations by year
- 2026: 2 · 2025: 1 · 2020: 1 · 2019: 2 · 2018: 1 · 2014: 1
- FWCI
- 1.26
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- IEEE International Conference on Acoustics Speech and Signal Processing (publishedVersion)
- HAL (submittedVersion)
- 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
- fractional delay filter, Padé approximants, continued fraction expansion, series expansion
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
