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Search results for: RESIDUE ARITHMETIC, RNS, CRT
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Scaling of numbers in residue arithmetic with the flexible selection of scaling factor
PublicationA scaling technique of numbers in resudue arithmetic with the flexible selection of the scaling factor is presented. The required scaling factor can be selected from the set of moduli products of the Residue Number System (RNS) base. By permutation of moduli of the number system base it is possible to create many auxilliary Mixed-Radix Systems associated with the given RNS with respect to the base, but they have different sets...
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Digital structures for high-speed signal processing
PublicationThe work covers several issues of realization of digital structures for pipelined processing of real and complex signals with the use of binary arithmetic and residue arithmetic. Basic rules of performing operations in residue arithmetic are presented along with selected residue number systems for processing of complex signals and computation of convolution. Subsequently, methods of conversion of numbers from weighted systems to...
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RNS/TCS CONVERTER DESIGN USING HIGH-LEVEL SYNTHESIS IN FPGA
PublicationAn experimental high-level synthesis (HLS) of the residue number system (RNS) to two’s-complement system (TCS) converter in the Vivado Xilinx FPGA environment is shown. The assumed approach makes use of the Chinese Remainder Theorem I (CRT I). The HLS simplifies and accelerates the design and implementation process, moreover the HLS synthesized architecture requires less hardware by about 20% but the operational frequency is smaller...
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HIGH LEVEL SYNTHESIS IN FPGA OF TCS/RNS CONVERTER
PublicationThe work presents the design process of the TCS/RNS (two's complement–to– residue) converter in Xilinx FPGA with the use of HLS approach. This new approach allows for the design of dedicated FPGA circuits using high level languages such as C++ language. Such approach replaces, to some extent, much more tedious design with VHDL or Verilog and facilitates the design process. The algorithm realized by the given hardware circuit is...
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On simplification of residue scaling process in pipelined Radix-4 MQRNS FFT processor
PublicationResidue scaling is needed in pipelined FFT radix-4 processors based on the Modified Quadratic Residue Number System (MQRNS) at the output of each butterfly. Such processor uses serial connection of radix-4 butterflies. Each butterfly comprises n subunits, one for each modulus of the RNS base and generates four complex residue numbers. In order to prevent arithmetic overflow intermediate results after each butterfly have to be...
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On configuration of residue scaling process in pipelined radix-4 MQRNS FFT processor
PublicationResidue scaling is needed in pipelined FFT radix-4 processors based on the Modified Quadratic Residue Number System (MQRNS) at the output of each butterfly. Such processor uses serial connection of radix-4 butterflies. Each butterfly comprises n subunits, one for each modulus of the RNS base and outputs four complex residue numbers. In order to prevent the arithmetic overflow in the succesive stage, every number has to be scaled,...
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FPGA realization of fir filter in residue arithmetic
Publicationw pracy zaprezentowano realizację fpga przepływowego filtru fir o stałych współczynnikach w arytmetyce resztowej z użyciem 8 5-bitowych modułów o łącznym zakresie liczbowym 37.07 bita. zastosowano formębezpośrednią fir. mnożenia wykonywane są przy użyciu odczytu z pamięci. sumowania w każdym z kanałów są realizowane przy zastosowaniu wielopoziomowej struktury sumatora opartego o 4-operandowe sumatory csa. w stopniu końcowym wykonywane...
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Pipelined division of signed numbers with the use of residue arithmetic in FPGA
PublicationAn architecture of a pipelined signed residue divider for small number ranges is presented. The divider makes use of the multiplicative division algorithm where initially the reciprocal of the divisor is calculated and subsequently multiplied by the dividend. The divisor represented in the signed binary form is used to compute the approximated reciprocal in the residue form by the table look-up. In order to reduce the needed length...
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Fpga implementation of the two-stage high-speed fir filter in residue arithmetic
Publicationw pracy przedstawiono implementację szybkiego, dwustopniowego kaskadowego filtru fir w technologii fpga z użyciem arytmetyki resztowej. zastosowanie arytmetyki resztowej pozwala na uzyskanie dużych częstotliwości potokowania w związku z użyciem małych mnożników. zalety arytmetyki resztowej są ograniczane w pewnym stopniu koniecznością wykonywania skalowania po pierwszym stopniu filtru celem uniknięcia nadmiaru arytmetycznego. w...
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FPGA realization of high-speed multi-stage FIR filter in residue arithmetic
PublicationW pracy przedstawiono implementację szybkiego wielostopniowego, kaskadowego filtru FIR w technologii FPGA. Zastosowanie arytmetyki resztowej pozwala na uzyskanie dużych częstotliwości próbkowania w zwiżaku z użyciem małych mnożników. Zalety wynikające z uzycia arytmetyki resztowej sa w pewnym stopniu ograniczne koniecznością wykonania skalowania przy kaskadowym połaczeniu filtrów FIR, tak aby uniknąć nadmiaru arytmetycznego. W...
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Pipelined division of signed numbers with the use of residue arithmetic for small number range with the programmable gate array
PublicationIn this work an architecture of the pipelined signed residue divider for the small number range is presented. Its operation is based on reciprocal calculation and multiplication by the dividend. The divisor in the signed binary form is used to compute the approximated reciprocal in the residue form by the table look-up. In order to limit the look-up table address an algorithm based on segmentation of the divisor into two segments...
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Scaling of signed residue numbers with mixed-radix conversion in FPGA with extended scaling factor selection
PublicationA scaling technique of signed residue numbers in FPGA is proposed. The technique is based on conversion of residue numbers to the Mixed-Radix System (MRS). The scaling factor is assumed to be a moduli product from the Residue Number System (RNS) base. Scaling is performed by scaling of MRS terms, the subsequent generation of residue representations of scaled terms, binary addition of these representations and generation of residues...
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Discrete convolution based on polynomial residue representation
PublicationThis paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS...
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Pipelined Two-Operand Modular Adders
PublicationPipelined two-operand modular adder (TOMA) is one of basic components used in digital signal processing (DSP) systems that use the residue number system (RNS). Such modular adders are used in binary/residue and residue/binary converters, residue multipliers and scalers as well as within residue processing channels. The structure of pipelined TOMAs is usually obtained by inserting an appropriate number of pipeline register layers within...
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Implementation of discrete convolution using polynomial residue representation
PublicationConvolution is one of the main algorithms performed in the digital signal processing. The algorithm is similar to polynomial multiplication and very intensive computationally. This paper presents a new convolution algorithm based on the Polynomial Residue Number System (PRNS). The use of the PRNS allows to decompose the computation problem and thereby reduce the number of multiplications. The algorithm has been implemented in Xilinx...
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Pipelined sceling of signed residue numbers with the mixed-radix conversion in the programmable gate array
PublicationIn this work a scaling technique of signed residue numbers is proposed. The method is based on conversion to the Mixed-Radix System (MRS) adapted for the FPGA implementation. The scaling factor is assumed to be a moduli product from the Residue Number System (RNS) base. Scaling is performed by scaling of terms of the mixed-radix expansion, generation of residue reprezentation of scaled terms, binary addition of these representations...
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FIReWORK: FIR Filters Hardware Structures Auto-Generator
PublicationThe paper presents application called FIReWORK, that allows for automatic creation of the VHDL hardware structures of FIR filters. Automat- ically generated specialized hardware solutions dedicated to the FPGA and ASIC are commonly known as Intellectual Property Cores. The essential fu- ture of the application is easy initialization of FIR filter parameters in GUI, and then automatically design, calculate and generate the IP Core...
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FPGA implementation of reverse residue conversion based on the new Chinese Remainder Theorem II- Part II,- Experimantal results
PublicationW pracy opisano realizację sprzętową konwertera z systemu resztowego do systemu binarnego. Konwerter jest oparty na nowej formie chińskiego twierdzenia o resztach CRT II. Teoretyczne aspekty takiej konwersji przedstawiono w części I. Implementację konwertera wykonano w środowisku Xilinx FPGA. Zaprezentowano ogólną architekturę konwertera, a także opisano realizację wybranych bloków. Podano ilość koniecznych zasobów sprzętowych...