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Wyszukujesz frazę "Residue Number System" wg kryterium: Temat


Tytuł:
The network coding method in wireless sensor networks based on residue number system
Metoda sieciowego kodowania danych w bezprzewodowych sieciach sensorowych na podstawie systemu resztowego
Autorzy:
Yatskiv, V
Powiązania:
https://bibliotekanauki.pl/articles/324351.pdf
Data publikacji:
2013
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
kodowanie danych
bezprzewodowa sieć sensorowa
system resztowy
data coding
wireless sensor network
residue number system
Opis:
The paper presents and investigates the method of network encoding in the residue number system for usage in wireless sensor networks. The method of encoding provides increase of total network bandwidth by choosing coprime digit capacity different modules and different routes of transmission residues.
W artykule zaproponowano i zbadano metodę kodowania sieciowego w systemie resztowym do stosowania w bezprzewodowych sieciach sensorowych. Opracowana metoda kodowania zwiększa ogólną przepustowość sieci dzięki wyborowi względnie pierwszych modułów o różnej pozycyjności i przesyłaniu reszt przez różne trasy.
Źródło:
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska; 2013, 67; 135-144
1641-3466
Pojawia się w:
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effective residue-to-binary converter with the Chinese Remainder Theorem
Efektywna konwersja liczb z systemu resztowego do systemu wagowego z uzyciem chińskiego twierdzenia o resztach
Autorzy:
Ulman, Z.
Czyżak, M.
Powiązania:
https://bibliotekanauki.pl/articles/152042.pdf
Data publikacji:
2003
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
cyfrowe przetwarzanie sygnałów
szybka arytmetyka komputerowa
resztowy system liczbowy
digital signal processing
fast computer arithmetic
residue number system
residue-to-binary converter
Opis:
The residue-to-binary conversion is the key operation in all digital signal processing applications that use the Residue Number System (RNS). In this work a new conversion technique based on the Chinese Remainder Theorem (CRT) for 5- and 6-bit moduli is proposed. It is especially suited for the realization with the use of binary arithmetic. the specific property of the realization with the use of binary arithmetic. The specific property of the technique is a way of calculation of the excess factor r in the CRT formula that makes possible, under certain conditions, the reduction of processed numbers from the range [0,nM) to [0,2M) where "M" is the product of moduli. This is done by replacing the calculation of "r" by the computation of the result of division of the sum of projections by a power of 2 close to M. Such approach allows for very effective hardware realization of the converter. Only small ROM`s and standard binary adders are required. Moreover, the pipelining on the Full-Adder (FA) level possible.
Konwersja liczb z systemu resztowego do systemu binarnego jest podstawową operacją we wszystkich układach cyfrowego przetwarzania sygnałów, które wykorzystują system resztowy. W niniejszej pracy zaproponowano nowa metodę konwersji opartą o chinskie twierdzenie o resztach dla modułów 5- i 6-bitowych. Specyficzną cechą nowej metody jest sposób obliczania tzw. współczynnika pomiaru "r" w formule chińskiego twierdzenia o resztach, co umożliwia pod pewnymi warunkami, redukcję przetwarzanych liczb z zakresu [0,nM) do [0,2M). Jest to realizowane poprzez zastąpienie obliczania "r" obliczaniem rB, gdzie M jest potęgą liczby 2 bliska M. Takie podejście pozwala na bardzo efektywną sprzętową realizację konwertora. Konieczne są tylko małe pamięci typu ROM i standardowe sumatory binarne. ponadto możliwa jest realizacja potokowa z częstotliwością ograniczoną opóźnieniem sumatora 1-bitowego.
Źródło:
Pomiary Automatyka Kontrola; 2003, R. 49, nr 12, 12; 34-38
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Scaling of numbers in residue arithmetic with the flexible selection of scaling factor
Autorzy:
Ulman, Z.
Czyżak, M.
Smyk, R.
Powiązania:
https://bibliotekanauki.pl/articles/376813.pdf
Data publikacji:
2013
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
scaling technique
scaling factor
residue arithmetic
Residue Number System
RNS
Mixed-Radix System
MRS
Opis:
A scaling technique of numbers in residue 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 auxiliary Mixed-Radix Systems (MRS). They serve as the intermediate systems in the scaling process. All MRS's are associated with the given RNS with respect to the base, but they have different sets of weights. For the scaling factor value resulting from the requirements of the given signal processing algorithm, the suitable MRS can be chosen that allows to obtain the scaling result in most simple manner.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2013, 76; 175-179
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
SIGN detection and signed integer comparison for three-moduli SET {2n ±1, 2n+k}
Autorzy:
Torabi, Zeinab
Timarchi, Somayeh
Powiązania:
https://bibliotekanauki.pl/articles/2097970.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
computer arithmetic
residue number system
signed integer comparison
dynamic range partitioning
Opis:
Comparison, division, and sign detection are considered to be complicated op erations in a residue number system (RNS). A straightforward solution is to convert RNS numbers into binary formats and then perform complicated op erations using conventional binary operators. If efficient circuits are provided for comparison, division, and sign detection, the application of RNS can be extended to those cases that include these operations. For RNS comparison in three-moduli set τ = {2 n−1, 2 n+k , 2 n+1},(0 ≤ k ≤ n), we have found only one hardware realization. In this paper, an efficient RNS comparator is proposed for moduli set τ , which employs a sign-detection method and operates more efficiently than its counterparts. The proposed sign detector and comparator utilize dynamic range partitioning (DRP), which has been recently presented for unsigned RNS comparison. The delay and cost of the proposed comparator are lower than the previous works, which makes it appropriate for RNS applications with limited delay and cost.
Źródło:
Computer Science; 2021, 22 (3); 387-401
1508-2806
2300-7036
Pojawia się w:
Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hierarchical residue number systems with small moduli and simple converters
Autorzy:
Tomczak, T.
Powiązania:
https://bibliotekanauki.pl/articles/907828.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
arytmetyka cyfrowa
układ cyfrowy
resztowy system liczbowy
digital arithmetic
digital circuits
residue number system
VLSI
Opis:
In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k š 1 and modulo 2k. The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k - 1, 2k, 2k +1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the use of the proposed HRNS depend on the possibility of factorisation of moduli [...].
Źródło:
International Journal of Applied Mathematics and Computer Science; 2011, 21, 1; 173-192
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Design of a complex multiplier based on the convolution with the use of the polynomial residue number system
Projektowanie mnożnika zespolonego oparte na splocie z użyciem wielomianowego systemu resztowego
Autorzy:
Smyk, R.
Czyżak, M.
Ulman, Z.
Powiązania:
https://bibliotekanauki.pl/articles/154071.pdf
Data publikacji:
2007
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
cyfrowe przetwarzanie sygnałów
mnożenie zespolone
wielomianowy system resztowy
digital signal processing
complex multiplication
polynomial residue number system
Opis:
The complex multiplication is one of the basic operations in digital signal processing. In this work the design procedure of the complex multiplier based on the well-known decomposition algorithm of Skavantzos and Stouraitis is presented. The algorithm makes use of encoding n-bit numbers as polynomials of degree 7 in the ring of polynomials modulo with -bit coefficients. The complex multiplication is carried out as an eight point cyclic convolution. The design procedure is illustrated by the computational example and design of a small multiplier.
Mnożenie zespolone jest jedną z podstawowych operacji w cyfrowym przetwarzaniu sygnałów. W niniejszej pracy przestawiono metodę projektowania mnożników zespolonych opartą na znanym algorytmie dekompozycji Skavantzosa and Stouraitisa. W algorytmie tym stosuje się kodowanie liczb n-bitowych jako wielomianów stopnia 7 w pierścieniu wielomianów modulo ze współczynnikami -bitowymi. Mnożenie zespolone jest następnie realizowane jako 8-punktowy splot cykliczny. Proponowaną metodę projektowania zilustrowano przykładem obliczeniowym oraz przykładowym projektem mnożnika.
Źródło:
Pomiary Automatyka Kontrola; 2007, R. 53, nr 4, 4; 68-71
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
High level synthesis in FPGA of TCS/RNS converter
Autorzy:
Smyk, R.
Czyżak, M.
Powiązania:
https://bibliotekanauki.pl/articles/377883.pdf
Data publikacji:
2017
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
high–level synthesis
residue number system
FPGA
C++ language
two's complement–to–residue converter
Opis:
The 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 represented as the program in C++. The performed design experiments had to show whether the obtained structures of TCS/RNS converter are acceptable with respect to speed and hardware complexity. The other aim of the work was to examine whether it is enough to write the program in C++ with the use of basic arithmetic operators or bit–level description is necessary. Finally, we present the discussion of results of the TCS/RNS converter design in Xilinx Vivado HLS environment.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2017, 91; 143-154
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On configuration of residue scaling process in pipelined radix-4 MQRNS FFT processor
Autorzy:
Smyk, R.
Czyżak, M.
Powiązania:
https://bibliotekanauki.pl/articles/377692.pdf
Data publikacji:
2014
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
fast Fourier transform
residue number system
modified quadratic residue number system
FFT pipelined processor
Opis:
Residue 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 the arithmetic overflow in the succesive stage, every number has to be scaled, i.e. divided by a certain constant. The dynamic range of the processed signal increases due to the summation within the butterfly and the transformation of coefficients of the FFT algorithm to integers. The direct approach would require eight residue scalers that would be highly ineffective regarding that such a set of scalers had to be placed after each butterfly. We show and analyze a structure which uses parallel-to-serial transformation of groups of numbers so that only two scalers are needed.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2014, 80; 145-150
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On simplification of residue scaling process in pipelined Radix-4 MQRNS FFT processor
Autorzy:
Smyk, R.
Czyżak, M.
Powiązania:
https://bibliotekanauki.pl/articles/97551.pdf
Data publikacji:
2014
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
fast Fourier transform
residue number system
modified quadratic residue number system
pipelined FFT processor
Opis:
Residue 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 scaled, i.e. divided by a certain constant. The number range of the processed signal increases due to transformation of coefficients of the FFT algorithm to integers and summation and multiplication within the butterfly. The direct approach would require eight residue scalers that would be highly ineffective regarding that such a set of scalers had to be placed after each butterfly. We show and analyze a structure which uses parallel-to-serial transformation of groups of numbers so that only two residue scalers are needed.
Źródło:
Computer Applications in Electrical Engineering; 2014, 12; 588-596
1508-4248
Pojawia się w:
Computer Applications in Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pipelined division of signed numbers with the use of residue arithmetic for small number range with the programmable gate array
Autorzy:
Smyk, R.
Ulman, Z.
Czyżak, M.
Powiązania:
https://bibliotekanauki.pl/articles/376378.pdf
Data publikacji:
2013
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
pipelining
residue number system
RNS
residue arithmetic
Opis:
In 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 algoritm based on segmentation of the divisor into two segments is used. The approximate reciprocal transformed to residue representation with the proper sign is stored in look-up tables. During operation it is multiplied by the dividend in the residue form and subsequently scaled. The pipelined realization of the divider in the FPGA environment is also shown.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2013, 76; 117-126
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
RNS/TCS converter design using high-level synthesis in FPGA
Wysokopoziomowa synteza konwertera RNS/U2 w FPGA
Autorzy:
Smyk, R.
Czyżak, M.
Powiązania:
https://bibliotekanauki.pl/articles/269200.pdf
Data publikacji:
2017
Wydawca:
Politechnika Gdańska. Wydział Elektrotechniki i Automatyki
Tematy:
Residue Number System
RNS
two's-complement system
TCS
Chinese Remainder Theorem I
CRT I
FPGA
system resztowy
system z uzupełnieniem do 2
U2
konwerter RNS/U2
chińskie twierdzenie o resztach
Opis:
An 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 by 30% than that for the VHDL designed converter.
W pracy przedstawiono eksperymentalną wysokopoziomową syntezę w FPGA konwertera L systemu resztowego do systemu reprezentacji z uzupełnieniem do 2 (U2). W zastosowanym podejściu wykorzystano algorytm konwersji na bazie chińskiego twierdzenia o resztach (CRT 1), Zauważono, że synteza wysokopoziomowa ułatwia proces projektowania oraz zauważalnie skraca czas testowania układu. Zaprojektowana architektura konwertera przy wykorzystaniu syntezy wysokopoziomowej pochłania o około 20% zasobów układu FPGA mniej niż dla konwertera zaprojektowanego przy użyciu języka VHDL, jednak maksymalna częstotliwość pracy jest niższa o około 30%.
Źródło:
Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej; 2017, 57; 121-126
1425-5766
2353-1290
Pojawia się w:
Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Scaling of signed residue numbers with mixed-radix conversion in FPGA with extended scaling factor selection
Autorzy:
Smyk, R.
Czyżak, M.
Ulman, Z.
Powiązania:
https://bibliotekanauki.pl/articles/97226.pdf
Data publikacji:
2013
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
residue number system
RNS
scaling
scaling algorithms
mixed-radix system
MRS
FPGA
Opis:
A 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 for all moduli. The sign of the residue number is detected by using the most significant digit of the MRS representation. Basic blocks of the scaler are realized in the form of modified two-operand modulo adders with included additional multiply and modulo reduction operations. An exemplary pipelined realization of the scaler in the Xilinx FPGA environment is shown. The design is based on Look-Up Tables (LUT)(2,sup>6 x 1) that simulate small RAMs which serve as main components for the look-up realization. Also a method is shown that allows for flexible selection of scaling factors from a set of moduli products of the RNS base. This is made by forming auxiliary MRSs by permutation of moduli of the base. All formed MRSs are associated with the given RNS with respect to the base but each MRS has different set of weights. Thus for the required scaling factor, the suitable MRS can be chosen that provides for the scaling error smaller than 1.
Źródło:
Computer Applications in Electrical Engineering; 2013, 11; 465-477
1508-4248
Pojawia się w:
Computer Applications in Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Residue number system (RNS)
Autorzy:
Sharoun, A. O.
Powiązania:
https://bibliotekanauki.pl/articles/376029.pdf
Data publikacji:
2013
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
residue number system
RNS
residue arithmetic
Opis:
In the residue number system, a set of moduli which are independent of each other is given. An integer is represented by the residue of each modulus and the arithmetic operations are based on the residues individually. The arithmetic operations based on residue number system can be performed on various moduli independently to avoid the carry in addition, subtraction and multiplication, which is usually time consuming. However, the comparison and division are more complicated and the fraction number computation is immatured. Due to this, a residue number system is not yet popular in general-purpose computers, though it is extremely useful for digital-signal-processing applications. This thesis deals with the design, simulation and microcontroller implementation of some (residue number system based) building blocks for applications in the field of digital signal processing. The building blocks which have been studied are binary to residue converter, residue to binary converter, residue adder and residue multiplier.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2013, 76; 265-270
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System
Autorzy:
Selianinau, Mikhail
Powiązania:
https://bibliotekanauki.pl/articles/1839284.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
residue number system
Chinese remainder theorem
residue code
rank of a number
positional characteristics
Opis:
The Chinese Remainder Theorem (CRT) widely used in many modern computer applications. This paper presents an efficient approach to the calculation of the rank of a number, a principal positional characteristic used in the Residue Number System (RNS). The proposed method does not use large modulo addition operations compared to a straightforward implementation of the CRT algorithm. The rank of a number is equal to a sum of an inexact rank and a two-valued correction factor that only takes on the values 0 or 1. We propose a minimally redundant RNS, which provides low computational complexity of the rank calculation. The effectiveness of the novel method is analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the extra residue modulo 2, the complexity of rank calculation goes down from \(O(k^2)\) to \(O(k)\), where \(k\) equals the number of residues in non-redundant RNS.
Źródło:
Computer Science; 2020, 21 (2); 225-240
1508-2806
2300-7036
Pojawia się w:
Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multifunctional unit for reverse conversion and sign detection based on five-moduli set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 }
Autorzy:
Mojahed, Mohsen
Molahosseini, Amir Sabbagh
Zarandi, Azadeh Alsadat Emrani
Powiązania:
https://bibliotekanauki.pl/articles/2097893.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
computer arithmetic
residue number system
reverse converter
Opis:
A high dynamic range moduli set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3} has recently been introduced as an arithmetically balanced five-modull set for the residue number system (RNS). In order to utilize this moduli set in applications handling signed numbers, two important components are needed: a sign detector, and a signed reverse converter. However, having both of these components results in high-hardware requirements, which makes RNS impractical. This paper overcomes this problem by designing a unified unit that can perform both signed reverse conversion as well as sign detection through the reuse of hardware. To the authors’ knowledge, this is the first attempt to design a sign detector for a moduli set that includes a {2 n 3} moduli. In order to achieve a hardwareamenable design, we first improved the performance of the previous unsigned reverse converter for this moduli set. Then, we extracted a sign-detection method from the structure of the reverse converter. Finally, we made an unsigned reverse converter-to-sign converter through the use of the extracted sign signal from the reverse converter. The experimental results show that the proposed reverse convertor and sign detector result in improvements of 31% and 28% in area and delay, respectively, as compared to the previous unsigned reverse convertor with sign output using a comparator.
Źródło:
Computer Science; 2021, 22 (1); 101-121
1508-2806
2300-7036
Pojawia się w:
Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł

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