A computationally efficient coefficient update technique for Lagrange fractional delay filters

Haghparast, Azadeh; Välimäki, Vesa

doi:10.1109/icassp.2008.4518465

Cited by 5 publications

(6 citation statements)

References 12 publications

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“…This implies that for any and that the formula in (5) can be applied to . So, since , it follows that: (10) with error bounded by . In summary, the coefficients can be used to approximate , provided the derivatives for are known using (10).…”

Section: Derivation Of a Barycentric Interpolator From The Coeffimentioning

confidence: 95%

“…So, since , it follows that: (10) with error bounded by . In summary, the coefficients can be used to approximate , provided the derivatives for are known using (10). In practice, however, this last condition is hardly fulfilled, but it is reasonable to employ (10) recursively, by substituting the values by the approximations which have already been computed using (10) itself.…”

Section: Derivation Of a Barycentric Interpolator From The Coeffimentioning

confidence: 95%

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Design of Barycentric Interpolators for Uniform and Nonuniform Sampling Grids

Selva

2010

IEEE Trans. Signal Process.

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This paper proposes a method to convert a fixed instant interpolator for band-limited signals into a variable instant one, which has the form of a barycentric interpolator. This interpolator makes it possible to approximate the signal and its derivatives with minimal complexity in a range that surrounds the initial instant, and is applicable to uniform and nonuniform sampling grids. The barycentric form of the interpolator is derived using two different procedures, first by the repeated use of Bernstein's inequality and Taylor's theorem, and second by truncating a Lagrange-type series. These procedures show that the proposed method can be applied to existing fixed instant interpolators, and that it can be accurate in long time intervals. Finally, an evaluation procedure for barycentric interpolators and their derivatives is presented that minimizes the number of divisions, solving at the same time the numerical problems associated with small denominators. This paper includes several numerical examples.

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Section: Derivation Of a Barycentric Interpolator From The Coeffimentioning

confidence: 95%

Section: Derivation Of a Barycentric Interpolator From The Coeffimentioning

confidence: 95%

Design of Barycentric Interpolators for Uniform and Nonuniform Sampling Grids

Selva

2010

IEEE Trans. Signal Process.

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“…This is because there is only one design parameter, that is, the polynomial order L. Most of the recently reported FD design methods belong to this time domain approach such as [16,17].…”

Section: Introductionmentioning

confidence: 99%

Frequency-Based Optimization Design for Fractional Delay FIR Filters with Software-Defined Radio Applications

Díaz-Carmona

Dolecek

Ramirez-Agundis

2010

International Journal of Digital Multimedia Broadcasting

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A frequency-designed fractional delay FIR structure, which is suitable for software radio applications, is presented. The design method is based on frequency optimization of a combination of modified Farrow and mutirate structures. As a result the optimization frequency range is made only in half of desired total bandwidth. According to the obtained results the proposed fractional delay structure allows online desired fractional delay update, with a high fractional delay value resolution.

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“…The most popular polynomial based technique for the closed-form designs of VFD filters is the maximally flat FIR filters [33][34][35][36][37][38][39][40][41][42][43][44]…”

Section: Closed-form Approachesmentioning

confidence: 99%

“…The conventional approaches for the polynomial approximation of VFD filters can be categorized into closed-form approaches and optimization approaches. In the closedform approaches [33][34][35][36][37][38][39][40][41][42][43][44][73][74][75][76][77], the Lagrange interpolation [33][34][35][36][38][39][40][41][42][43] is the most attractive technique because it can approximate the required fractional delays accurately if only fractional delays at low frequency are concerned [49]. Many researches have been done to exploit the relations between the filter coefficients to reduce the filter implementation complexity, and the original Farrow structure is modified such that the structure can be used to implement the Lagrange interpolation VFD filter [33-36, 38, 39].…”

Section: Introductionmentioning

confidence: 99%

Design and implementation of variable digital filters with low computational complexity

Xu¹

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frequency response error, phase error, phase delay error and group delay error. However, in the most common applications of the VFDs, the time domain instantaneous delayed samples are estimated. In this thesis, for such applications, the relations between the above frequency domain errors (in particular the frequency response error, phase error and group delay error), and the time domain errors are investigated. The design criteria of the VFD filters for this particular application are identified. Besides the investigation on the design criteria, a new VFD filter design approach is proposed. In this approach, the full band input signal is split into several subbands by a newly proposed filter bank. By shifting each subband a proper phase, the VFD is realized by combining necessary subbands. The proposal VFD technique can be incorporated with the variable bandedge characteristic with little extra complexity. Hence, the filters with simultaneously variable bandedges and fractional delays (VBFDs) are obtained. In the design of the VBFD filters, the split subbands can be either kept or discarded to form the variable bandedges. However, this requires the bandwidth of the individual band of the filter bank to be narrower than the transition bandwidth of the VBFD filters. By introducing a shaping filter to the last retained band to form the transition band of the VBFD filters, the bandwidth of the individual band of the filter bank may be relaxed to about twice of the transition bandwidth of the VBFD filters. Compared with the existing VBFD filter design techniques, the proposed approaches significantly reduce the computational complexity of the VBFD filters.

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A computationally efficient coefficient update technique for Lagrange fractional delay filters

Cited by 5 publications

References 12 publications

Design of Barycentric Interpolators for Uniform and Nonuniform Sampling Grids

Design of Barycentric Interpolators for Uniform and Nonuniform Sampling Grids

Frequency-Based Optimization Design for Fractional Delay FIR Filters with Software-Defined Radio Applications

Design and implementation of variable digital filters with low computational complexity

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