Radix-4 DFT butterfly realization with the use of the modified quadratic residue number system

• Autorzy: Czyżak M. , Smyk R.
• Konferencja: Computer Applications in Electrical Engineering 2010 [Poznań, April 19-21, 2010]
• Języki publikacji: EN

Abstrakty

EN

The paper presents the design and implementation of the radix-4 DFT butterfly with the use of the complex residue number system (CRNS) the modified quadratic residue number system(MQRNS). The MQRNS in addition to the decompositional property of the residue number system allows for the realization of the complex multiplication with three real multiplications. In the Xilinx FPGA Virtex 6 for the 5-bit CRNS base the implementation of multiplications, additions and modulo operations can be based on 6-bit ROM's realized with (2⁶x 1) LUT's. The radix-4 DFT butterfly formula is transformed so that the DFT transforms values are 4-operand sums of the input numbers with the succesive complex multiplications. In the first stage the 4-operand modulo m additions are performed, then the required CRNS/MQRNS conversions are done. In the following stage the MQRNS multiplications are performed with the succeeding reverse MQRNS/CRNS conversion. Such configuration allows to attain high pipelining frequencies.

Słowa kluczowe

EN

DFT; complex residue number system; CRNS; modified quadratic residue number system; MQRNS

PL

DFT; dyskretna transformata Fouriera; CRNS; MQRNS

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Poznan University of Technology Academic Journals. Electrical Engineering
• Rocznik: 2010
• Tom: No. 63
• Strony: 39--49
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Czyżak M.

autor

Smyk R.

• Gdansk University of Technology

Bibliografia

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• [5] Szabo N.S., Tanaka R.J. : Residue Arithmetic and its Applications to Computer Technology, New York, McGraw-Hill, 1967.
• [6] Krishnan R., Jullien G.A., Miller W.C.: The modified quadratic residue number system (MQRNS) for complex high-speed signal processing, IEEE Trans, on Circuits and Systems, 1986, no.3, pp. 325-327.