Design of FIR first order digital differentiatorsof variablefractional sample delay using maximally flat error criterion

Hermanowicz, E.; Rojewski, M.

doi:10.1049/el:19940009

Cited by 13 publications

(8 citation statements)

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“…The proposed method can be also extended to design differentiator with factional delay which has been studied in [33]. Fact 1 can be generalized as follows.…”

Section: E Discussionmentioning

confidence: 99%

“…Using the L'Hopital rule and (15), the can be computed by (40) If we choose the parameters in (9) of [33] as , then the coefficients in (9) of [33] are exactly same as the coefficients in (40). This is because both are maximally flat design.…”

Section: E Discussionmentioning

confidence: 99%

“…In this method, the fractional delay is approximated by (33) So far, the weighted least squares and minimax methods have been proposed to design subfilters such that this approximation is as well as possible. If we choose , then (33) will reduce to (34) Now, let us use the Farrow structure to design differentiator.…”

Section: Design Based On Farrow Structurementioning

confidence: 99%

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Digital differentiator design using fractional delay filter and limit computation

Tseng

2005

IEEE Trans. Circuits Syst. I

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In this paper, the design of digital differentiator is investigated. First, the relation between fractional delay filter and first-order differentiator is established such that the differentiator can be obtained from fractional delay filter by using the computation of limit. Then, conventional finite-impulse response (FIR), allpass and Farrow-based fractional delay filters are directly applied to design first-order differentiator. Next, the proposed method is extended to design high-order differentiators. Finally, several design examples are illustrated to demonstrate the effectiveness of this new design approach.Index Terms-Allpass filter, digital differentiator, farrow structure, finite-impulse response (FIR) filter, fractional delay filter, infinite-impulse response (IIR) filter.

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“…The proposed method can be also extended to design differentiator with factional delay which has been studied in [33]. Fact 1 can be generalized as follows.…”

Section: E Discussionmentioning

confidence: 99%

Section: E Discussionmentioning

confidence: 99%

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Digital differentiator design using fractional delay filter and limit computation

Tseng

2005

IEEE Trans. Circuits Syst. I

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“…Using the two original filters and , the linearly interpolated filter can be obtained by a weighted average of the two transfer functions, such that (9) It is not possible to obtain an interpolated IIR filter from two IIR filters without increasing the filter order unless all the poles of the two original filters are common. For the general case where all the poles of the original filters are different, an interpolated filter can only be obtained at the cost of doubling the filter order.…”

Section: B Comparison With Linear Interpolationmentioning

confidence: 99%

“…Most frequently used fractional-delay filters are finite-impulse-response (FIR) filters based on Lagrange interpolation [8], [9]. The Farrow structure [5] allows continuously varying the fractional delay using a single parameter.…”

Section: Introductionmentioning

confidence: 99%

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

Hachabiboglu

Günel

Kondoz

2007

IEEE Trans. Signal Process.

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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.

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Fractional Delay Filters—Design and Applications

Välimäki¹,

Laakso²

2001

Nonuniform Sampling

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Design of FIR first order digital differentiatorsof variablefractional sample delay using maximally flat error criterion

Cited by 13 publications

References 1 publication

Digital differentiator design using fractional delay filter and limit computation

Digital differentiator design using fractional delay filter and limit computation

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

Fractional Delay Filters—Design and Applications

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