The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
Results on Maximally Flat Fractional-Delay Systems
Abstract
The two classes of maximally flat finite-impulse response (FIR) and all-pass infinite-impulse response (IIR) fractional-sample delay systems are thoroughly studied. New expressions for the transfer functions are derived and mathematical properties revealed. Our contributions to the FIR case include a closed-form formula for the Farrow structure, a three-term recurrence relation based on the interpolation algorithm of Neville, a concise operator-based formula using the forward shift operator, and a continued fraction representation. Three types of structures are developed based on these formulas. Our formula for the Farrow structure enhances the existing contributions by Valimaki, and by Vesma and Sarama/spl uml/ki on the subsystems of the structure. For the IIR case, it is rigorously proved, using the theory of Pade approximants, that the continued fraction formulation of Tassart and Depalle yields all-pass fractional delay systems. It is also proved that the maximally flat all-pass fractional-delay systems are closely related to the Lagrange interpolation. It is shown that these IIR systems can be characterized using Thiele's rational interpolation algorithm. A new formula for the transfer function is derived based on the Thiele continued fractions. Finally, a new class of maximally flat FIR fractional-sample delay systems that exhibit an almost all-pass magnitude response is proposed. The systems possess a maximally flat group-delay response at the end frequencies 0 and /spl pi/, and are characterized by a closed-form formula. Their main advantage over the classical FIR Lagrange interpolators is the improved magnitude response characteristics.
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 [18]
Citations
Cites
Concrete Mathematics: A Foundation for Computer Science
Graham, R. L., Knuth, D. E., Patashnik, O., & Liu, S. (1989) · Computers in Physics · doi:10.1063/1.4822863 · Cited by 2,406
Applied and Computational Complex Analysis
Thacher, H. C., & Henrici, P. (1977) · Mathematics of Computation · doi:10.2307/2005805 · Cited by 2,055
The Special Functions and Their Approximations
Clenshaw, C. W., & Luke, Y. L. (1972) · Mathematics of Computation · doi:10.2307/2004747 · Cited by 1,478
Analytic Theory of Continued Fractions
Wall, H. S. (1967) · Cited by 1,438
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
The Calculus of Finite Differences
(1934) · Students Quarterly Journal · doi:10.1049/sqj.1934.0017 · Cited by 831
A continuously variable digital delay element
Farrow, C. W. (2003) · 1988., IEEE International Symposium on Circuits and Systems · doi:10.1109/iscas.1988.15483 · Cited by 816
Die Lehre von den Kettenbrüchen
Perron, O. (1977) · Vieweg+Teubner eBooks · doi:10.1007/978-3-663-01496-6 · Cited by 634
A Table of Series and Products
Hansen, E. R. (1975) · International Linear Collider · Cited by 581
Applied and Computational Complex Analysis.
Auslander, L., & Henrici, P. (1988) · American Mathematical Monthly · doi:10.2307/2323585 · Cited by 516
The Special Functions and their Approximations
(1969) · Mathematics in Science and Engineering/Mathematics in science and engineering · doi:10.1016/s0076-5392(09)x6004-2 · Cited by 327
Sequence Transformations and their Applications.
Wynn, P. H., & Wimp, J. (1982) · Mathematics of Computation · doi:10.2307/2007352 · Cited by 307
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
Applied and computational complex analysis
Frank, E. (1980) · Journal of the Franklin Institute · doi:10.1016/0016-0032(80)90048-4 · Cited by 223
Kunz, K. S. (1957) · Cited by 177
Discrete-Time Modeling of Acoustic Tubes Using Fractional Delay Filters
V�lim�ki, V. (1998) · Cited by 123
A new variable fractional sample delay filter with nonlinear interpolation
Liu, G.-S., & Wei, C.-H. (1992) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/82.205818 · Cited by 100
Explicity formulas for weighting coefficients of maximally flat tunable FIR delays
Hermanowicz, E. (1992) · Electronics Letters · doi:10.1049/el:19921239 · Cited by 93
Optimization and efficient implementation of FIR filters with adjustable fractional delay
Vesma, J., & Saramäki, T. (2002) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1997.612771 · Cited by 86
FIR approximation of fractional sample delay systems
Kootsookos, P. J., & Williamson, R. C. (1996) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/82.486473 · Cited by 79
A new filter implementation strategy for Lagrange interpolation
Välimäki, V. (2002) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1995.521525 · Cited by 70
On Interpolation by Iteration of Proportional Parts, without the Use of Differences
Aitken, A. C. (1932) · Proceedings of the Edinburgh Mathematical Society · doi:10.1017/s0013091500013808 · Cited by 69
A simple design of maximally flat delay digital filters
Fettweis, A. (1972) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1972.1162355 · Cited by 56
Pei, S.-C., & Wang, P.-H. (2001) · IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications · doi:10.1109/81.917976 · Cited by 53
Universal maximally flat lowpass FIR systems
Samadi, S., Nishihara, A., & Iwakura, H. (2000) · IEEE Transactions on Signal Processing · doi:10.1109/78.847782 · Cited by 44
Self-citationProgrammable fractional sample delay filter with Lagrange interpolation
Liu, G.-S., & Wei, C.-H. (1990) · Electronics Letters · doi:10.1049/el:19901031 · Cited by 33
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
Analytical approximations of fractional delays: Lagrange interpolators and allpass filters
Tassart, S., & Depalle, P. (2002) · 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing · doi:10.1109/icassp.1997.599673 · Cited by 27
Explicit Nearly Optimal Linear Rational Approximation with Preassigned Poles
Stenger, F. (1986) · Mathematics of Computation · doi:10.2307/2008091 · Cited by 26
FIR digital filters with simultaneous conditions on amplitude and delay
Baher, H. (1982) · Electronics Letters · doi:10.1049/el:19820202 · Cited by 22
A note on the fir approximation of a fractional sample delay
Minocha, S., Roy, S. C. D., & Kumar, B. (1993) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.4490210306 · Cited by 19
Harris, F. (2002) · Asilomar Conference on Signals, Systems and Computers (ACSSC) · doi:10.1109/acssc.1997.679201 · Cited by 13
Generation of digital transfer functions of the FIR type approximating z/sup -p/q/
Ramachandran, V., Gargour, C. S., & Ahmadi, M. (2002) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1990.112707 · Cited by 10
Response of maximally flat lowpass filters to polynomial signals
Samadi, S., & Nishihara, A. (2002) · doi:10.1109/iscas.2001.921014 · Cited by 4
Self-citationSalzer, H. E. (1980) · Mathematics of Computation · doi:10.1090/s0025-5718-1980-0551310-4 · Cited by 2
Misstatements in Milne-Thomson, Calculus of Finite Differences, Macmillan, London, 1933
Salzer, H. E. (1980) · Mathematics of Computation · doi:10.2307/2006240 · Cited by 1
Flagged first, then by citations
Research works printed but not linked: 4
- Neville, 1934, Iterative interpolation, J. Indian Math. Soc., 20, 87
- de Lagrange, Sur l’usage des fractions continues dans le calcul intégral, Oeuvres, 4, 301
- Gauss, Disquisitiones generales circa seriem infinitam $1 + ({{\alpha\beta }/{ 1\cdot\gamma }})x + ({{\alpha (\alpha +1)\beta (\beta +1) }/{ 1\cdot 2\cdot\gamma (\gamma +1)}}) x x + ({{\alpha (\alpha\!+\!1)(\alpha\!+\!2)\beta (\beta\!+\!1) (\beta\!+\!2)}/{ 1\!\cdot\! 2\!\cdot\! 3\!\cdot\!\gamma (\gamma\!+\!1)(\gamma\!+\!2)}}) x^{3}\!+$ etc., Gauss Werke, 3, 134
- 10.1090/S0025-5718-1986-0842132-0 · DOI
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
Design of fractional delay filter using discrete Fourier transform interpolation method
Tseng, C.-C., & Lee, S.-L. (2010) · Signal Processing · doi:10.1016/j.sigpro.2009.10.016 · Cited by 34
$H^{\infty}$-Optimal Fractional Delay Filters
Nagahara, M., & Yamamoto, Y. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2265678 · Cited by 15
“This ideal low-pass filter is however not realizab le because of its non-causality and instability, and hence man y studies have focused their attention on approximating the i deal filter by, for example, windowed sinc functions [15], [16], maximally-flat FIR approximation [17], [18], [19], [20], [2 1], all-pass appro…”
BackgroundA 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
- Samadi, S., Ahmad, M. O., & Swamy, M. N. S.
- Affiliations
- Concordia University (CA)
- Venue
- IEEE Transactions on Circuits and Systems I: Regular Papers
- Published
- 2004-11
- Volume
- 51
- Issue
- 11
- Pages
- 2271-2286
- ISSN
- 1057-7122 (ISSN-L)
- OpenAlex
- W2161486443
- Cited by
- 51
- References
- 37
- Citations by year
- 2020: 1 · 2019: 4 · 2017: 4 · 2016: 1 · 2015: 2 · 2014: 2 · 2013: 5 · 2012: 3
- FWCI
- 6.80
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Analog and Mixed-Signal Circuit Design
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Keywords
- maximally flat filters, FIR filters, all-pass filter, Farrow structure, Padé approximants, Lagrange interpolation, group delay, magnitude response, transfer function
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
