SVD-Based Design and New Structures for Variable Fractional-Delay Digital Filters

Deng, Tian-Bo; Nakagawa, Yasuhiro

doi:10.1109/tsp.2004.831922

Cited by 104 publications

(34 citation statements)

References 24 publications

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“…Some coefficients g l (n) have a negligible effect on the overall system performance and can be fixed to be zero valued. 4 Observation 2. After fixing some coefficient values to be equal to zero according to Observation 1, for l even (odd), there exist some values of n for which the sums of the values of all the existing g l (n)'s in Figure 1 for l even (odd) are very close to zero.…”

Section: Filter Optimizationmentioning

confidence: 98%

“…During the last two decades, numerous methods have been proposed for designing adjustable fractional delay FIR filters with infinite-precision coefficients [1], [4], [5], [9]- [11], [24], [25], [27], [29], [30]. These methods include, among others, a constrained minimax optimization [27], [29], a Taylor series expansion (b) Direct-form implementation for G l (z) of order 2M − 1 for l even.…”

Section: Introductionmentioning

confidence: 99%

“…This reduction can be achieved by properly sharing these 2M − 1 delay terms between the G l (z)'s. [9], [24], [30], a singular value decomposition [4], and weighted least-squares designs [1], [10], [25]. More synthesis techniques can be found in a tutorial article [11].…”

Section: Introductionmentioning

confidence: 99%

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Multiplication-Free Polynomial-Based FIR Filters with an Adjustable Fractional Delay

Yli‐Kaakinen

Saramäki

2006

Circuits Syst Signal Process

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An efficient coefficient quantization scheme is described for minimizing the cost of implementing fixed parallel linear-phase finite impulse response (FIR) filters in the modified Farrow structure introduced by Vesma and Saramäki for generating FIR filters with an adjustable fractional delay. The implementation costs under consideration are the minimum number of adders and subtracters when implementing these parallel subfilters as a very large-scale integration (VLSI) circuit. Two implementation costs are under consideration to meet the given criteria. In the first case, all the coefficient values are implemented independently of each other as a few signed-powers-of-two terms, whereas in the second case, the common subexpressions within all the coefficient values included in the overall implementation are properly shared in order to reduce the overall implementation cost even further. The optimum finite-precision solution is found in four steps. First, the number of filters and their (common odd) order are determined such that the given criteria are sufficiently exceeded in order to allow some coefficient quantization errors. Second, those coefficient values of the subfilters having a negligible effect on the overall system performance are fixed to be zero valued. In addition, the experimentally observed attractive connections between the coefficient values of the subfilters, after setting some coefficient values equal to zero, are utilized to reduce both the implementation cost and the parameters to be optimized even more. Third, constrained nonlinear optimization is applied to determine for the remaining infinite-precision coefficients a parameter space that includes the feasible space where the given criteria are met. The fourth step involves finding in this space the desired finite-precision coefficient values for minimizing the given implementation costs to meet the stated overall criteria. Several examples are included illustrating the efficiency of the proposed synthesis scheme. *

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Section: Filter Optimizationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Multiplication-Free Polynomial-Based FIR Filters with an Adjustable Fractional Delay

Yli‐Kaakinen

Saramäki

2006

Circuits Syst Signal Process

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“…Based on the frequency response (9) of the denominator , we obtain the frequency response of the allpass VFD filter (2) as (10) where denotes the complex conjugate. By considering the correspondence i.e., (11) between the actual variable frequency response and the desired one, we can simplify the correspondence as (12) which implies that we must use to approximate If the above approximation is well achieved, i.e., (13) then (14) Using the identity the approximation in (14) can be rewritten as (15) which indicates (16) Therefore, we only need to minimize the error . From we obtain (17) Consequently, the optimal coefficient matrix of the allpass VFD filter (2) can be found by minimizing the weighted squared error (18) where is a nonnegative weighting function.…”

Section: A Design Problem Formulationmentioning

confidence: 99%

“…The survey paper [9] details some designs, implementations, and applications of fixed fractional-delay (FFD) filters as well as VFD filters. So far, many methods have been developed for designing and implementing finite-impulse response (FIR) VFD filters because it is relatively easy to formulate the FIR VFD filter design problem and get the optimal solutions [10]- [14]. In contrast, allpass VFD filters are much more difficult to design because the stability problem must be taken into account and the design of allpass VFD filters usually involves nonlinear optimization or iterative procedures.…”

Section: Introductionmentioning

confidence: 99%

Non-iterative WLS Design of Allpass Variable Fractional-Delay Digital Filters

Deng

2005 IEEE International Symposium on Circuits and Systems

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Abstract-This paper presents a noniterative weighted-leastsquares (WLS) method for designing allpass variable fractional-delay (VFD) digital filters. After expressing each coefficient of an allpass VFD filter as a polynomial of the VFD parameter , we develop a noniterative technique for finding the optimal polynomial coefficients, and show that the allpass VFD filter design problem can be efficiently solved without using any iterative procedure while a closed-form solution can be easily obtained through solving a matrix equation. Compared with the existing iterative WLS method that solves a series of approximately linearized WLS minimization problems, the proposed noniterative one can yield much better design results with significantly reduced computational complexity. Moreover, the new WLS method does not involve any convergence issue.Index Terms-Allpass variable fractional-delay (VFD) digital filter, iterative weighted-least-squares (WLS) design, noniterative WLS design, VFD digital filter, WLS design.

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Optimal design of symmetric fractional delay filter using firefly algorithm

Srivastava

Dwivedi

Nagaria

2020

Circuit Theory & Apps

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Summary A fractional delay filter is used to increase the accuracy, preciseness, time synchronization, and stability of signal processing system. However, designing a fractional delay filter for a specified delay, without affecting spectral characteristics of the signal is challenging because of nondifferentiability and multimodal nature of its objective function. In this paper, a more accurate design technique has been proposed for designing fractional delay filters, based on a recently developed firefly algorithm and its improved version. The designed filters offer variable fractional delay. A novel symmetric structure of implementation has been used to design filters. The efficacy of the proposed technique is evaluated by considering a filter design example. The performance of the proposed technique is compared with the other exiting algorithm. The comparative analysis of finite impulse response (FIR) fractional delay filter design proves that the proposed algorithm has a smaller design error and an implementation complexity than the other reported existing algorithms. In addition to this, the designed FIR fractional delay filter is implemented on Xilinx Virtex‐7 for experimental validation.

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SVD-Based Design and New Structures for Variable Fractional-Delay Digital Filters

Cited by 104 publications

References 24 publications

Multiplication-Free Polynomial-Based FIR Filters with an Adjustable Fractional Delay

Multiplication-Free Polynomial-Based FIR Filters with an Adjustable Fractional Delay

Non-iterative WLS Design of Allpass Variable Fractional-Delay Digital Filters

Optimal design of symmetric fractional delay filter using firefly algorithm

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