• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.9
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• pp.2121-2126
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• 2013

This paper compares radix-2 based structures for 32768-point FFT. Radix-$2^k$ structures have been widely used because the butterfly is simple and the number of multipliers can be reduced in those structures. This paper applied various radix-$2^k$ structures to 32768-point FFT that is representing ultra-long FFT. The ultra-long FFT has been studied much recently. This paper shows that the radix-$2^4$ structure is the most adequate because it shows the smallest complexity in the synthesis and the best SQNR performance. should be placed here.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.5
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• pp.84-93
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• 2007

In this paper, a Radix-8 structure for high-speed FFT is propose. Main block of the proposed FFT structure is Radix-8 DIF(Decimation In Frequency) butterfly. Even throughput of the Radix-8 FFT is twice than that of the Radix-4 FFT, implementation area of the Radix-8 is larger than that of Radix-4 FFT. But, implementation area of the proposed Radix-8 FFT was reduced by using DA(Distributed Arithmetic) for multiplication. For comparison, the 64-point FFT was implemented using conventional Radix-4 butterfly and proposed Radix-8 butterfly, respectively. The Verilog-HDL coding results for the proposed FFT structure show 49.2% cell area increment comparison with those of the conventional Radix-4 FFT structure. Namely, to speed up twice, 49.2% of area cost is required. In case of same throughput, power consumption of the proposed structure is reduced by 25.4%. Due to its efficient processing scheme, the proposed FFT structure can be used in large size of FFT like OFDM Modem.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.8
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• pp.5579-5585
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• 2015

In FFT(Fast Fourier Transform) implementation, DIT(Decimation-In-Time) and DIF (Decimation-In-Frequency) methods are mostly used. Among them, various DIF structures such as Radix-2/4/8 algorithm have been developed. Compared to the DIF, the DIT structures have not been investigated even though they have a big advantage producing a sequential output. In this paper, a butterfly structure for DIT Radix-8 algorithm is proposed. The proposed structure has smaller latency time because of Radix-8 algorithm in addition to the advantage of the sequential output. In case of 4096-point FFT implementation, the proposed structure has only 4 stages which shows the smaller latency time compared to the 12 stages of Radix-2 algorithm. The proposed butterfly can be used in FFT block required the sequential output and smaller latency time.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.45 no.3
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• pp.103-110
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• 2008

In this paper, an efficient butterfly structure for 8K/2K-Point Radix-4 FFT algorithm using CORDIC(coordinate rotation digital computer) is proposed. It is shown that CORDIC can be efficiently used in twiddle factor calculation of the Radix-4 FFT algorithm. The Verilog-HDL coding results for the proposed CORDIC butterfly structure show 36.9% cell area reduction comparison with those of the conventional multiplier butterfly structure. Furthermore, the 8K/2K-point Radix-4 pipeline structure using the proposed butterfly and delay commutators is compared with other conventional structures. Implementation coding results show 11.6% cell area reduction. Due to its efficient processing scheme, the proposed FFT structure can be widely used in large size of FFT like OFDM Modem.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.49 no.3
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• pp.8-14
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• 2012

In this paper, a low-area FFT structure using $Radix-4^2$ algorithm is proposed. The large point FFT structure consists of cascade connection of the many stages. In implementation of large point FFT using $Radix-4^2$ algorithm, stages which number of different coefficients are only 3 appear in every 2 stages. For example, in the 4096-point FFT, the stages that number of different coefficients are 3 appear in stage 1, 3, and 5 among 6 stages. Multiplication block area of these 3 stages can be reduced using CSD(Canonic Signed Digit) and common sub-expression sharing techniques. Using the proposed structure, the 256-point FFT is implemented with the Verilog-HDL coding and synthesized by $1.971mm^2$ cell area in tsmc $0.18{\mu}m$CMOS library. This result shows 23% cell area reduction compared with the conventional structure.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.1
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• pp.683-690
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• 2015

Two basic FFT(Fast Fourier Transform) algorithms are the DIT(Decimation-In-Time) and the DIF (Decimation-In-Frequency). In spite of the advantage of the DIT algorithm is to generate a sequential output, various structures have not been made. In this paper, a new DIT Radix-4 FFT butterfly structure are proposed and implemented using Verilog coding. Through synthesis, it is shown that the 64-point FFT is implemented by 6.78 million gates. Since the proposed FFT structure has the advantage of a sequential output, it can be used in OFDM communication SoC(System on a Chip) which need a high speed FFT output.

• Proceedings of the Korea Information Processing Society Conference
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• 2005.05a
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• pp.1777-1780
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• 2005

OFDM(Orthogonal Frequency Division Multiplexing)은 제 4 세대 기술로 일컬어지는 변조 방식으로 최근 유럽의 디지털 오디오 방송(DAB)과 디지털 비디오 방송(DVB)에 표준으로 사용되고 있으며, IEEE 802.11a 무선 LAN 및 디지털 가입자라인 xDSL 에서도 사용되고 있다. 본 논문에서는 OFDM 모뎀 구현의 핵심이라고 할 수 있는 64-포인트 FFT(Fast Fourier Transform) 프로세서의 여러 가지 구조를 분석하고, 이들과 비교하여 성능 대 면적 비를 획기적으로 향상시킨 새로운 FFT 프로세서인 Radix-4,2 SIC (Single Instruction Computer) 구조를 제안하였다. 본 논문에서 제안하는 SIC 구조는 버터플라이 연산의 재사용을 극대화하였으며 Radix-4,2 알고리즘을 사용함으로써 FFT 프로세서에서 면적의 80%를 차지하는 복소곱셈기의 수를 감소시켜 크기를 획기적으로 줄인 결과를 보여 준다.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.85-86
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• 2007

In this paper, a Radix-8 structure for high-speed FFT is proposed. Even throughput of the Radix-8 FFT is twice than that of the Radix-4 FFT, implementation area of the Radix-8 is larger than that of Radix-4 FFT. But, implementation area of the proposed Radix-8 FFT was reduced by using DA(Distributed Arithmetic) for multiplication. The Verilog-HDL coding results for the proposed FFT structure show 49.2% cell area increment comparison with those of the conventional Radix-4 FFT structure. Namely, to speed up twice, 49.2% of area cost is required. In case of same throughput, power consumption of the proposed structure is reduced by 25.4%.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.4
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• pp.1867-1875
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• 2011

In this paper, a low-area 256-point FFT structure is proposed. For low-area implementation CSD(Canonic Signed Digit) multiplier method is chosen. Because multiplication type should be less for efficient CSD multiplier application to the FFT structure, the Radix-$4^2$ algorithm is chosen for those purposes. After, in the proposed structure, the number of multiplication type is minimized in each multiplication block, the CSD multipliers are applied for implementation of multiplication. Furthermore, in CSD multiplier implementation, cell-area is more reduced through common sub-expression sharing(CSS). The Verilog-HDL coding result shows 29.9% cell area reduction in the complex multiplication part and 12.54% cell area reduction in overall 256-point FFT structure comparison with those of the conventional structure.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.4A
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• pp.539-545
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• 2000

A 40-Mb/s, 64-state, R= 1/2, 3 bit soft decision Viterbi decoder based on Radix-4 method has been designed and fabricated using a FLEX10K CPLD chip in this paper. In order to implement the high-speed Viterbi decoder, the architectures of adder-compare-select(ACS), branch metric calculation(BMC), trace back(TB) are present. In practical designed by ASIC, the speed is faster than that of CPLD by 6~7 times. Therefore, 40 Mb/s Viterbi decoder architecture can be used for high-speed wireless multimedia communications with 200 Mb/s.