Recursive digital filters with maximally flat group delay

Thiran, J. P.

doi:10.1109/tct.1971.1083363

Cited by 217 publications

(99 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The only known class of realizable filters having explicit formulas of their coefficients as a function of is the class of Thiran filters [41], [44].…”

Section: All-pass Fractional Delay Fltersmentioning

confidence: 99%

Reversible, Fast, and High-Quality Grid Conversions

Condat

Ville

Forster-Heinlein

2008

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

Abstract-A new grid conversion method is proposed to resample between two 2-D periodic lattices with the same sampling density. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into (at most) three successive shear operations. The translations along the shear directions are implemented by 1-D fractional delay operators, which revert to simple 1-D convolutions, with appropriate filters that yield the property of symmetric reversibility. We show that the method is fast and provides high-quality resampled images. Applications of our approach can be found in various settings, such as grid conversion between the hexagonal and the Cartesian lattice, or fast implementation of affine transformations such as rotations.

show abstract

“…The only known class of realizable filters having explicit formulas of their coefficients as a function of is the class of Thiran filters [41], [44].…”

Section: All-pass Fractional Delay Fltersmentioning

confidence: 99%

Reversible, Fast, and High-Quality Grid Conversions

Condat

Ville

Forster-Heinlein

2008

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

show abstract

“…As originally shown by Thiran [11], it is possible to express the denominator polynomial of a maximally flat group-delay filter as a truncated Gauss hypergeometric series defined as (39) where is the Gamma function [25]. Let us consider the two -order original filters having the respective set of coefficients, , and , approximating delays and , such that .…”

Section: Transient Errors and Dfii Thiran Fractional-delay Filtersmentioning

confidence: 99%

“…There exist design methods based on optimization for obtaining allpass fractional delay filters [10] which are computationally costly for real-time operation. One of the simplest design methods to obtain maximally flat delay allpass fractional-delay filters is by using the Thiran approximation [11], [12]. Consider an -order allpass IIR filter having the following transfer function:…”

Section: Introductionmentioning

confidence: 99%

“…Using the Thiran approximation, the coefficients of an -order allpass fractional-delay filter that approximates the total fractional delay can be calculated using the following closed-form formula [1]: (4) The filter with the given coefficients is guaranteed to be stable and to have maximally flat group delay corresponding to the desired fractional delay, , at low frequencies [11]. Using (4), the calculation of the coefficient requires multiplications and a single division excluding the computation of the binomial term.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Root Displacement Interpolation Method for Tunable Allpass Fractional-Delay Filters

Hachabiboglu

Günel

Kondoz

2007

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-One of the simplest ways of designing allpass fractional-delay filters with maximally flat group delays is by using the Thiran approximation by which the filter coefficients are calculated using a closed-form equation. However, due to the number of multiplications and divisions involved, the calculation of these coefficients is a computationally costly task and is not suitable for real-time applications. The analysis of a root-displacement-based interpolation method used in allpass tunable fractional delays is presented in this paper. The method allows continuous adjustments of the approximated fractional delay without the explicit calculation of a new set of filter coefficients. The transient error observed at the output due to the change of filter coefficients is analyzed. The direct and cascade implementations are compared with respect to their transient errors. An example application of the proposed method from the field of model-based sound synthesis is given.

show abstract

“…Major drawback in the great majority of those is the computational complexity required to obtain the filter coefficients. A simple allpass fractional-delay filter can be obtained by the Thiran approximation [9,10]. However, it is not as straightforward with Thiran fractional-delay filters as the Farrow structure to continuously modify the fractional-delay.…”

Section: Introductionmentioning

confidence: 99%

Interpolated Allpass Fractional-Delay Filters Using Root Displacement

Hacıhabiboğlu

Günel

Kondoz

2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings

View full text Add to dashboard Cite

Fractional-delay filter is the general name given to filters modelling non-integer delays. Such filters have a flat phase delay for a wide frequency band, with the value of the phase delay approximating the fractional delay. A maximally-flat delay IIR fractional-delay filter can be obtained by the Thiran approximation. A simple and efficient method for obtaining filters modelling intermediate fractional delays from two Thiran fractional-delay filters is proposed. The proposed method allows continuously modifying the fractional delay. Computational complexity of the proposed method is discussed. A practical application of the method in model-based sound synthesis is given as an example.

show abstract

Recursive digital filters with maximally flat group delay

Abstract: A well-known limitation of the recursive digital tllter, when amplitude, phase, and transient responses, are given.'

Cited by 217 publications

References 6 publications

Reversible, Fast, and High-Quality Grid Conversions

Reversible, Fast, and High-Quality Grid Conversions

Analysis of Root Displacement Interpolation Method for Tunable Allpass Fractional-Delay Filters

Interpolated Allpass Fractional-Delay Filters Using Root Displacement

Contact Info

Product

Resources

About