Implementation of non-positional digital filters

Veligosha, A. V.; Linets, G. I.; Kaplun, Dmitry; Klionskiy, Dmitry M.; Bogaevskiy, D. V.

doi:10.1109/scm.2016.7519711

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…The second group includes the methods and algorithms of digital filtering based on residue number codes. Multiple studies [11][12][13] have described the methods for constructing non-positional digital filters that are based on algebraic structures, possessing the properties of ring and field.…”

Section: Of 14mentioning

confidence: 99%

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

et al. 2018

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This paper introduces a method for optimizing non-recursive filtering algorithms. A mathematical model of a non-recursive digital filter is proposed and a performance estimation is given. A method for optimizing the structural implementation of the modular digital filter is described. The essence of the optimization is that by using the property of the residue ring and the properties of the symmetric impulse response of the filter, it is possible to obtain a filter having almost a half the length of the impulse response compared to the traditional modular filter. A difference equation is given by calculating the output sample of modules p1 … pn in the modified modular digital filter. The performance of the modular filters was compared with the performance of positional non-recursive filters implemented on a digital signal processor. An example of the estimation of the hardware costs is shown to be required for implementing a modular digital filter with a modified structure. This paper substantiates the expediency of applying the natural redundancy of finite field algebra codes on the example of the possibility to reduce hardware costs by a factor of two. It is demonstrated that the accuracy of data processing in the modular digital filter is higher than the accuracy achieved with the implementation of filters on digital processors. The accuracy advantage of the proposed approach is shown experimentally by the construction of the frequency response of the non-recursive low-pass filters.

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Section: Of 14mentioning

confidence: 99%

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

et al. 2018

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“…Therefore, one of the ways to significantly increase the speed and decrease the computing power in these algorithms is to utilize the residue number system. RNS usually is used for applications such as digital signal processing [11,12], digital filters [13,14], image processing [15,16], and error correction systems [17,18].…”

Section: Introductionmentioning

confidence: 99%

Efficient Implementation Of The Sum Of Residues Modular Reduction Using Arithmetic-Friendly RNS Moduli Set

Alvani

2024

EATP

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Introduction: Due to the importance of public-key cryptography in information and communication security, it is widely employed in various applications for secure communication. Materials and Methods: multiplication and exponentiation of large numbers are used in cryptography algorithms such as RSA, ElGamal, and elliptic curve cryptography. Results and Discussion: The residue number system in these algorithms is very efficient since calculations are performed on small residues, resulting in a fast arithmetic operation, as well as lower power consumption. The modular reduction of large numbers is one of the main operations in most public-key cryptography systems, which includes large computations in finite fields. This paper presents an efficient implementation of modular reduction. To this end, arithmetic-friendly moduli were selected and employed in the implementation of the improved sum of residues reduction algorithm. The SOR algorithm using the proposed moduli set was described in VHDL language and synthesized on the Xilinx virtex7 FPGA family using ISE14.7 software. Conclusion:The results showed that, compared to the recent similar works, the implementation of the improved sum of residues algorithm using the proposed moduli set has achieved higher speed and uses less hardware resources.

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“…Unlike addition, subtraction and multiplication operations, dividing, sign detection, and comparing values are difficult to do in RNS. This system is broadly utilized in special-purpose processors to run applications such as public key cryptography algorithm [2][3][4], RSA [5][6][7][8], Elliptic Curve Cryptography (ECC) [9][10][11][12][13][14], digital signal processing (DSP) [15][16][17][18][19], digital filters [20][21][22][23], image processing [24][25][26], and error correction systems [27][28][29][30]. The primary operation in cryptography algorithms such as RSA and ECC, is the modular multiplication on large numbers [12,31,32].…”

Section: Introductionmentioning

confidence: 99%

Fast And Area-Efficient Reverse Converters For Five ModuliSet {2n+1, 2n-1-1, 2n, 2n+1-1, 2n-1}

Alvani

2024

EATP

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Introduction:This paper proposes two new reverse converters for balanced and wellformed five-moduli set {2 n +1, 2 n-1 -1, 2 n , 2 n+1 -1, 2 n -1}. The converters are planned in a twolevel architecture while appreciating adder base structures without utilizing any ROM, which results in an efficient implementation in VLSI circuits. Materials and Methods: To design both levels of the proposed reverse converters, Mixed-Radix Conversation (MRC) algorithm is employed. Results and Discussion: Unit gate delay and area estimation demonstrate the proposed reverse converter (DC1) is faster than other alternatives, the similar five moduli reverse converter, under distinctive dynamic ranges while the second design (DC2) requires less hardware cost. Conclusion:The synthesis results on Xilinx Virtex-7 FPGA illustrate that, comparing to the latest five moduli set reverse converters, the proposed converter (DC1) has achieved 11%, 12% and 11% improvement in speed for n = 12, 16 and 20, respectively.

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Implementation of non-positional digital filters

Cited by 4 publications

References 3 publications

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

Efficient Implementation Of The Sum Of Residues Modular Reduction Using Arithmetic-Friendly RNS Moduli Set

Fast And Area-Efficient Reverse Converters For Five ModuliSet {2n+1, 2n-1-1, 2n, 2n+1-1, 2n-1}

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