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본 논문은 OFDM 시스템을 위한 효율적인 가변길이 radix-8/4/2 FFT 구조를 제안하였다. radix-8/4/2 연산을 수행하기 위해서 제안한 FFT 프로세서는 shared memory 구조를 사용하여 하드웨어가 단순하고 적은 면적을 차지한 다. 메모리 사이즈를 줄이고 데이터들 간의 충돌을 피하기 위해 효율적인 In-place 메모리 엑세스 방법을 제안한다. 또한 회전인자(twiddle factor)를 위한 ROM 기반의 lookup 테이블 방식을 대신하여 적은 면적을 차지하는 회전인자 발생기를 제안한다. 제안한 FFT 프로세서는 802.11a, 802.16a, DAB, DVB-T/H 그리고 xDSL에서 요구하는 모든 FFT 샘플링 포인트인 64, 256, 512, 1024, 2048, 4096 그리고 8192 포인트의 FFT 연산을 할 수 있다.

In this paper, we propose an efficient variable-length radix-8/4/2 FFT architecture for OFDM systems. The FFT processor is based on radix-8 FFT algorithm and also supports radix-4 or radix-2 FFT computation. We are using efficient “In-place” memory access method to maintain conflict-free data access and minimize memory size. Also we replace a very large lookup table with a twiddle factor generator which consumes less area then a ROM-based lookup table. The proposed FFT processor performs variable-length FFT including 64, 256, 512, 1024, 2048, 4096 and 8192 points which cover all the required FFT lengths used in 802.11a, 802.16a, DAB, DVB-T, VDSL and ADSL.

A novel architecture FFT processor which can carry on 1-D FFT algorithm or 2-D FFT algorithm corresponding different size of FFT is proposed in this paper. The architecture is served as a scalable IP Core which is suitable for the heterogeneous multi-core SoC on chip application. The mixed architecture FFT processor achieves balance between high processing speed and resources. Compared with a conventional 1-D FFT processor, this FFT processor is characterized by having smaller resources consumption; compared with a 2-D FFT processor which is mapped onto a long point FFT architecture, it has higher processing speed. It employs the Radix-2 DIT-FFT algorithm and fixed addressing structure. It takes two ways to hide time consumed on data-path, one is read-ahead operation of dual-port RAM to hide the delay introduced by 12-stages pipeline of butterfly-unit and Memory access delay; the other is Ping-Pong operation of 3 groups of RAM to conceal data transmitting time. It also adopt twiddle factor compression algorithm to reduce ROM space. It can carry out 2n (n is from range of 5 to 14) single-precision floating-point FFT/IFFT directly. As a result, we have implemented the mixed architecture FFT processor based on FPGA, and successfully applied it into the heterogeneous multi-core SoC.

In this paper, the design of decimation in time Radix-2 FFT processor is presented, which is integrated in FPGA chip, regarding FPGA as design carrier. New butterfly-shaped operation method is proposed based on the traditional FFT algorithm and the analysis of hardware unit, which can reduce multiplication. And it adopted the Look-up table method. The results of hardware test of FFT processor shows that the processor works well and has high speed, and the design was realized by using FPGA.

A parallel and pipelined Fast Fourier Transform (FFT) processor for use in the Orthogonal Frequency division Multiplexer (OFDM) and WLAN, unlike being stored in the traditional ROM. The twiddle factors in our pipelined FFT processor can be accessed directly. A novel simple address mapping scheme and the modified radix 4 FFT also proposed. FPGA was majorly used to develop the ASIC IC’s to which was implemented. Here we simulated and synthesized the 256- point FFT with radix-4 using VHDL coding and 64 point FFT Hardware implementation we designed code using System C. Finally, the pipelined 256-point FFT processor can be completely implemented within 19.103ns.

본 논문에서는 IEEE 802.16e mobile WiMax 시스템을 위한 효율적인 FFT 프로세서 구조를 제안한다. 제안된 scalable FFT/IFFT 프로세서는 128/512/1024/2048-point FFT 연산을 가변적으로 수행할 수 있다. 또한 mixed radix (MR) 기법과 multi- path delay commutator (MDC) 구조를 사용하여 비단순 승산을 줄임으로써 기존의 설계 구조에 비해 시스템 수율 변화 없이 하드웨어 복잡도를 크게 감소시켰다. 제안된 scalable FFT/IFFT 프로세서는 하드웨어 설계 언어 (HDL)를 이용하여 설계 되었고, 0.18um CMOS 스탠다드 셀 라이브러리를 이용하여 논리 합성되었다. 논리합성 결과 4채널 radix-2 MDC (R2MDC) FFT 프로세서와 비교시 16% 감소된 게이트 수와 27% 감소된 메모리로 구현 가능함이 확인되었다.

In this paper, an area-efficient FFT processor is proposed for IEEE 802.16e mobile WiMax systems. The proposed scalable FFT processor can support the variable length of 128, 512, 1024 and 2048. By reducing the required number of non-trivial multipliers with mixed-radix (MR) and multi-path delay commutator (MDC) architecture, the complexity of the proposed FFT processor is dramatically decreased without sacrificing system throughput. The proposed FFT processor was designed in hardware description language (HDL) and synthesized to gate-level circuits using 0.18um CMOS standard cell library. With the proposed architecture, the gate count for the processor is 46K and the size of memory is 64Kbits, which are reduced by 16% and 27%, respectively, compared with those of the 4-channel radix-2 MDC (R2MDC) FFT processor.

In this paper, the FFT processor for power measurement using VHDL (Very high-speed integrated circuit Hardware Description Language) is discussed. The proposed system relies on the FFT algorithm to compute real and reactive power. The advantage of system is that harmonic analysis is carried out on a period of the Input signal. The proposed system is based on FFT Processor which is designed using VHDL. In the design of FFT processor, $radix-2^2$ is adopted to reduce several complex multipliers for twiddle factor. And this processor adopt pipeline structure. Therefore, the system Is able to have both high hardware efficiency and high performance.

In this paper, we designed a 256-point FFT processor using VHDL. We adopted Radix-2$^2$SDC(Single-path Delay Commutator) architectures to reduce the number of complex multipliers. We confirmed the operation of the design through simulation using Altera MAX+PLUS II.

This paper presents a high-throughput low-complexity 512-point eight-parallel mixed-radix multipath delay feedback (MDF) fast Fourier transform (FFT) processor architecture for orthogonal frequency division multiplexing (OFDM) applications. To decrease the number of twiddle factor (TF) multiplications, a mixed-radix $2^4/2^3$ FFT algorithm is adopted. Moreover, a dual-path shared canonical signed digit (CSD) complex constant multiplier using a multi-layer scheme is proposed for reducing the hardware complexity of the TF multiplication. The proposed FFT processor is implemented using TSMC 90-nm CMOS technology. The synthesis results demonstrate that the proposed FFT processor can lead to a 16% reduction in hardware complexity and higher throughput compared to conventional architectures.

In this paper, we present a fast Fourier transform (FFT) processor with four parallel data paths for multiband orthogonal frequency-division multiplexing ultra-wideband systems. The proposed 128-point FFT processor employs both a modified radix-$2^4$ algorithm and a radix-$2^3$ algorithm to significantly reduce the numbers of complex constant multipliers and complex booth multipliers. It also employs substructure-sharing multiplication units instead of constant multipliers to efficiently conduct multiplication operations with only addition and shift operations. The proposed FFT processor is implemented and tested using 0.18 ${\mu}m$ CMOS technology with a supply voltage of 1.8 V. The hardware- efficient 128-point FFT processor with four data streams can support a data processing rate of up to 1 Gsample/s while consuming 112 mW. The implementation results show that the proposed 128-point mixed-radix FFT architecture significantly reduces the hardware cost and power consumption in comparison to existing 128-point FFT architectures.

본 논문은 높은 데이터 처리율을 요하는 MIMO-OFDM 시스템을 위하여 고속의 낮은 하드웨어 복잡도를 가진 128/64-point $radix-2^4$ FFT/IFFT 프로세서 설계에 대해 제안한다. 높은 Radix 다중경로 지연 피드백 (MDF) FFT구조는 고속의 데이터 처리율과 낮은 하드웨어 복잡도를 제공한다. 제안하는 프로세서는 128-point와 64 Point FFT/IFFT의 동작을 지원할 뿐만 아니라 4-병렬 데이터 경로를 사용함으로써 높은 데이터 처리율을 지원한다. 또한, 제안하는 프로세서는 기존의 128/64-point FFT/IFFT 프로세서에 비해 낮은 하드웨어 복잡도를 지닌다. 제안된 FFT/IFFT 프로세서는 IEEE 802.11n 표준의 요구사항을 만족시키며 140MHz 클락 속도에서 560MSample/s의 높은 데이터 처리율을 가진다.

This paper presents a novel high-speed, low-complexity flexible 128/64-point $radix-2^4$ FFT/IFFT processor for the applications in high-throughput MIMO-OFDM systems. The high radix multi-path delay feed-back (MDF) FFT architecture provides a higher throughput rate and low hardware complexity by using a four-parallel data-path scheme. The proposed processor not only supports the operation of FFT/IFFT in 128-point and 64-point but can also provide a high data processing rate by using a four-parallel data-path scheme. Furthermore, the proposed design has a less hardware complexity compared with traditional 128/64-point FFT/IFFT processors. Our proposed processor has a high throughput rate of up to 560Msample/s at 140MHz while requiring much smaller hardware expenditure satisfying IEEE 802.11n standard requirements.

레이다 시스템의 경우, 타겟의 거리와 속도를 추출하기 위해 FFT (fast Fourier transform) 연산이 필수적으로 요구되며, 실시간 구현을 위해 고속으로 동작하는 FFT 프로세서의 설계가 필요하다. 고속 FFT 프로세서를 위한 하드웨어 구조로 완전 셔플 네트워크 (perfect shuffle network) 구조가 적합하며, 특히 초고속 연산을 위해 radix-4 기반의 이중 완전 셔플 네트워크 (twice perfect shuffle network) 구조가 가장 적절하고 볼 수 있다. 더불어, 다양한 속도 해상도를 요구하는 레이다 응용을 고려할 때, FFT 프로세서는 가변길이 FFT 연산을 지원할 필요가 있다. 이에 본 논문에서는 8~1024 포인트의 가변 길이 연산을 지원하는 이중 완전 셔플 네트워크 기반의 FFT 알고리즘을 제안하였으며, 이의 하드웨어 구조 설계 및 구현 결과를 제시한다. 제안된 FFT 프로세서는 HDL (hardware description language)을 활용하여 RTL (register transfer level) 설계가 수행되었으며, $0.65{\mu}m$ CMOS 공정을 활용하여 논리 합성한 결과, 총 3,293K개의 논리 게이트로 구현 가능함을 확인 할 수 있었다.

In radar systems, FFT (fast Fourier transform) operation is necessary to obtain the range and velocity of target, and the design of an FFT processor which operates at high speed is required for real-time implementation. The perfect shuffle network is suitable for high-speed FFT processor. In particular, twice perfect shuffle network based on radix-4 is preferred for very high-speed FFT processor. Moreover, radar systems that requires various velocity resolution should support scalable FFT points. In this paper, we propose a 8~1024-point scalable FFT processor based on twice perfect shuffle network algorithm and present hardware design and implementation results. The proposed FFT processor was designed using hardware description language (HDL) and synthesized to gate-level circuits using $0.65{\mu}m$ CMOS process. It is confirmed that the proposed processor includes logic gates of 3,293K.

본 논문에서는 기존 2진 FFT(Fast fourier transform)에서 확장해 다치논리 연산기를 이용해서 고속 다치 FFT 연산기를 구현하였다. 이를 바탕으로 구현한 FFT 연산의 가산은 기존의 2치 FFT연산과 비교해 결선과 트랜지스터 개수도 반으로 줄어지는 효과가 있다. 캐리 전파없는 가산기를 구현하기 위해서 (0,1,2,3)의 과잉 디지트 집합을 이용한 과잉 양의 수 표현(Reduntandt Positive-digit number Representation)을 FFT 내부적으로 이용하였고 이로 인해 능동소자의 감소와 이를 연결하기 위한 결선의 감소의 효과가 있고 VLSI(Very large scale intergation)의 설계시 정규성과 규칙성으로 효과적이다. FFT의 가산동작을 위해서는 캐리전파없는 가산기를 사용하였고 그리고 곱셉작용을 위해서는 곰셉기의 연산시간이 길고 면적이 큼으로 간단한 수학적 동작을 위해서 다치 LUT(Look up table)을 이용해 곱셈의 역할을 대신하였다. 마지막으로 시스템의 호환을 위해 하이브리드형 다치 FFT 연산기를 설계하여 예로 제시하였다.

The use of Multiple-Valued FFT(Fast fourier Transform) is extended from binary to multiple-valued logic(MVL) circuits. A multiple-valued FFT circuit can be implemented using current-mode CMOS techniques, reducing the transitor, wires count between devices to half compared to that of a binary implementation. For adder processing in FFT, We give the number representation using such redundant digit sets are called redundant positive-digit number representation and a Redundant set uses the carry-propagation-free addition method. As the designed Multiple-valued FFT internally using PD(positive digit) adder with the digit set 0,1,2,3 has attractive features on speed, regularity of the structure and reduced complexities of active elements and interconnections. for the mutiplier processing, we give Multiple-valued LUT(Look up table)to facilitate simple mathmatical operations on the stored digits. Finally, Multiple-valued 8point FFT operation is used as an example in this paper to illuatrates how a multiple-valued FFT can be beneficial.

본 논문에서는 OFDM 시스템용 복조기의 구현에 가장 핵심적인 소자인 2K/4K/8K-point FFT 프로세서를 제안하였다. 구현된 프로세서는 30MHz 시스템 클럭에 서 8,192개의 복소 입력 샘플을 273㎲에 2,048개의 복소 입력 샘플을 68.26㎲에 수행함으로써 OFDM방송에서 요구하는 심볼 fp이트의 데이터를 처리할 수 있다. 기본 구조는 1차원 DFT를 작은 크기의 2차원 DFT로 변환할 수 있는 쿨리-투키 알고리듬을 적용하였으며 다차원 DFT 변환에 적합한 전치 메모리와 셔플 메모리를 사용하였다. 복소 곱셈기는 기존의 방법보다 더 효율적인 메모리 구조를 갖는 CORDIC 프로세서를 사용하였으며 제안하는 트위들팩터 발생 방법은 트위들팩터를 저장하기 위한 ROM의 크기를 효과적으로 줄일 수 있다.

This paper present the architecture and design of FFT processor for the OFDM modulation. The OFDM modulation have a merit that use frequecncy efficiently and robust ISI. It needs FFR to have fast and large number of points. Moreover, this FFT design has pipeline architecture. R2$^2$SDF architecture for FFT processor has more advantage others. Therefore this paper present FFT processor used R2$^2$SDF architecture.

This paper describes 16-point FFT processor using systolic array and its implementation into VLSI. Designed FFT processor executes FFT/IFFT arithmetic under mode control and consists of cell array, array controller and input/output buffer memory. For design for testibility, we added built-in self test circuit into designed FFT processor. To verify designed 16-point FFT processor, logic simulation was performed by YSLOG on MICRO-VAXII. From the simulation results, it is estimated that the proposed FFT processor can perform 16-point FFT in about 4400[ns].

본 논문에서는 고속 데이터 전송을 위한 OFDM 시스템에 적용 가능한 고속 FFT 프로세서를 제안하였다. 8개의 병렬 경로를 가지는 MDC 파이프라인 고속 FFT 프로세서를 제안한다. 제안하는 구조는 연산과 하드웨어의 최적화를 위해 radix-$2^6$ 알고리즘에 기반하고 있다. 하드웨어 복잡도를 감소시키기 위해서 상수 곱셈기와 교환기 구조를 제안하고 새로운 스케즐링 기법을 적용하였다. 제안하는 FFT 프로세서는 새로운 구조를 적용해 지연 소자와 연산 사이클의 증가 없이 복소 곱셈기 및 연산복잡도를 감소시킬 수 있다. 또한 최적화한 twiddle factor $W_{64}$ 상수 곱셈기는 기존 복소 booth 곱셈기에 비해 65%만의 하드웨어 복잡도를 보였다. 설계한 FFT 프로세서는 Verilog HDL로 모델링하여 IBM 90nm 공정으로 합성하였으며 $0.27mm^2$의 면적과 388MHz의 주파수에서 2.7 GSample/s를 보이고 있다.

This paper proposed the new eight-parallel MDC FFT processor using the eight-parallel MDC architecture and the efficient scheduling scheme. The proposed FFT processor supports the 256-point FFT based on the modified radix-$2^6$ FFT algorithm. The proposed scheduling scheme can reduce the number of complex multipliers from eight to six without increasing delay buffers and computation cycles. Moreover, the proposed FFT processor can be used in OFDM systems required high throughput and low hardware complexity. The proposed FFT processor has been designed and implemented with a 90nm CMOS technology. The experimental result shows that the area of the proposed FFT processor is $0.27mm^2$. Furthermore, the proposed eight-parallel MDC FFT processor can achieve the throughput rate up to 2.7 GSample/s at 388MHz.

본 논문에서는 의료 서비스를 위한 뇌전기파(EEG : electroencephalogram) 신호 분석용 FFT(Fast Fourier Transform) 프로세서를 구현하였다. 실시간으로 발생하는 긴 신호를 short-time FFT 처리하기 위해 Hamming 창 함수를 사용하였으며, 이로 인해 감소되는 양끝의 값은 1/2 오버랩 시켜주어 보완하였다. 0~100[Hz] 사이의 주파수 특성을 가지는 뇌전기파의 효율적인 대역 분석을 위해 256-point FFT 프로세서를 radix-4 알고리듬을 적용하여 구현하였고, 단일 메모리 뱅크 구조를 사용하여 집적도를 높였다. 설계된 FFT 프로세서는 연산오차가 3% 이내로 높은 연산 정밀도를 갖는다.

This paper describes a design of fast Fourier transform(FFT) processor for EEG(electroencephalogram) signal analysis for health care services. Hamming window function with 1/2 overlapping is adopted to perform short-time FFT(ST-FFT) of a long period EEG signal occurred in real-time. In order to analyze efficiently EEG signals which have frequency characteristics in the range of 0 Hz to 100 Hz, a 256-point FFT processor based on single-memory bank architecture and radix-4 algorithm is designed. The designed FFT processor has high accuracy with arithmetic error less than 3%.

In this paper, power quality analysis system is proposed where voltage or current waveforms are nonsinusoidal. The proposed system relies on the FFT algorithm to compute real and reactive power. The advantage of system is that harmonic analysis is carried out on a period of the input signal. The proposed system is based on FFT processor which is designed using VHDL(Very high-speed integrated circuit Hardware Description Language). In the design of FFT processor, radix- $2^2$ is adopted to reduce several complex multipliers for twiddle factor. Complex multiplier is implemented as only shifters and adders. Therefore, the system is able to have both high hardware efficiency and high performance.