一种实序列FFT算法改进及其在DSP上的实现

FFT是数字信号处理最重要的算法之一,论文分析了常规的2N点按时间抽选的实序列FFT运算的基本原理,介绍了一种改进的算法,算法将奇数序列和偶数序列部分开计算,并提取旋转因子的公因子,大大减少了计算过程中的加法和乘法的个数和旋转因子的引用次数,并在实际的DSP平台上进行了实现,实验数据表明,该算法在运算效率和复杂度上都较传统FFT算法有较大的改进。     

基于FPGA的混合基FFT算法设计与实现

目前,研究资源节约型的低复杂度混合基快速傅里叶变换(FFT)设计技术具有重要的应用价值。本文基于现场可编程逻辑门阵列(FPGA)平台提出并实现了一种新型混合基FFT分解算法。该算法基于原位存储结构设计,采用素数因子分解与库利-图基分解相结合的混合分解模式,在省去了一步旋转因子乘法运算的同时也有效减小了存储空间和运算量,并采用通用蝶形单元模块设计使得算法能够同时适应基2、基3、基4的FFT运算。仿真结果表明,该算法可以极大提高FFT处理点数的灵活性,有效节省运算资源。     

3780点FFT处理器的研究

3780点FFT模块是地面数字多媒体／电视广播传播系统（DMB—T）中的重要模块之一，由于该模块不能直接利用现已成熟的基-2和基-4的算法，故给出了三种实现3780点FFT的算法和处理器结构，分别是内插成4096点的FFT算法、混合基FFT算法和综合分解算法，并对各种方法的优缺点进行了讨论。     

基于FPGA的4k点基-16FFT模块的实现

针对高速实时处理的要求,提出了4096点快速傅立叶变换(FFT)模块在现场可编程门阵列(FPGA)中的设计和实现。在运算模块中,基于按频率抽取基-4算法提出了一种新型的基-16蝶型算法,并采用八级流水结构和四路转换器来实现。本文采用块浮点和循环存储结构,避免了溢出和节省了大量的硬件资源。实验结果表明,该方法在保证了运算精度和实现复杂度的同时,使运算速度相对于基-4算法提高了1倍。     

高基FFT处理器高效地址产生算法

FFT算法是数字信号处理最常用算法,使用FFT处理器是进行FFT运算的重要手段之一。本文针对主基16局部流水的FFT处理器,提出了一种运用于高基FFT处理器的新型地址产生结构,能够进行16~4096点可变长的FFT运算,具有快速灵活的特点,且结构简单,适合FFT处理器中对数据通路控制的实现。     

一种无线局域网专用高性能FFT处理器设计

针对基8算法提出一种无冲突地址生成方法,设计了802.11a专用FFT处理器,整体采用流水处理,实现了一种高性能FFT硬件架构,各级RAM采用乒乓操作,每个RAM均由8个独立的SRAM存储体组成,通过对循环移位寄存器译码,蝶算单元并行无冲突读写RAM操作数,8通道输入数据并行处理,每级运算所需的时钟周期大幅度降低.FFT运算连续输入、输出,数据运算精度通过块浮点得到保证.整体具有高速、高精度的特征.本文提出的无冲突地址生成方法也可以扩展至高点数FFT的应用.     

长序列信号快速相关及卷积的算法研究

文章通过对快速傅立叶变换（FFT）的算法原理分析,根据线性相关和卷积的数学特征及物理含义,针对长序列信号,提出了一种基于FFT的长序列快速相关及卷积算法,用C＋＋进行了算法编程,在计算机上得到较好的实验效果,提高了运行速度,并结合算术傅立叶变换进行了改进。     

基于FFT的星上多路FDMA/FSK信号解调研究

提出了一种基于FFT的星上多路FDMA/FSK信号解调算法。首先分析了该算法的基本原理,证明了其性能与FSK信号理想非相干解调性能相同,同时提出了利用FFT进行频差估计的算法;对系统进行了性能仿真,仿真结果与理论分析一致;该算法实现简单、复杂度低,适合星上处理。     

FFT算法的一种FPGA设计

在分析了快速傅里叶算法理论的基础上,提出了一种频率抽取基4FFT的FPGA设计方案,针对现有FFT的FPGA实现过程中蝶形运算需要频繁乘以多个旋转因子提出了改进方法,减少了旋转因子的乘法次数和存储空间,加快了蝶形运算的速度,设计的地址映射方法,无需运算即可得到所需数据的存放地址,并结合采用乒乓结构和流水线方式,来提高快速傅里叶变换(FFT)FPGA实现的速度,为实现FFT算法提供了一定的参考价值。     

基于CORDIC的FFT处理器设计

波束形成是阵列信号处理过程的一个重要步骤,它在雷达、地质勘探、医学成像领域起着关键的作用并得到了广泛的应用。在声呐系统中,FFT处理器是波束形成器的关键部件,论文中引用了CORDIC算法,并对比了基2、基4等时域FFT算法的区别,根据基本原理和流程最终选定了基4算法,将其有效地和CORDIC算法结合起来。设计了一款基于CORDIC算法的FFT处理器。采用流水线方式,形成了5级蝶形算法,满足了FFT运算要求。     

New continuous-flow mixed-radix (CFMR) FFT Processor using novel in-place strategy

The paper proposes a new continuous-flow mixed-radix (CFMR) fast Fourier transform (FFT) processor that uses the MR (radix-4/2) algorithm and a novel in-place strategy. The existing in-place strategy supports only a fixed-radix FFT algorithm. In contrast, the proposed in-place strategy can support the MR algorithm, which allows CF FFT computations regardless of the length of FFT. The novel in-place strategy is made by interchanging storage locations of butterfly outputs. The CFMR FFT processor provides the MR algorithm, the in-place strategy, and the CF FFT computations at the same time. The CFMR FFT processor requires only two N-word memories due to the proposed in-place strategy. In addition, it uses one butterfly unit that can perform either one radix-4 butterfly or two radix-2 butterflies. The CFMR FFT processor using the 0.18 /spl mu/m SEC cell library consists of 37,000 gates excluding memories, requires only 640 clock cycles for a 512-point FFT and runs at 100 MHz. Therefore, the CFMR FFT processor can reduce hardware complexity and computation cycles compared with existing FFT processors.     

An Area-Efficient Design of Variable-Length Fast Fourier Transform Processor

Fast Fourier transform (FFT) plays an important role in the orthogonal frequency division multiplexing (OFDM) communication systems. In this paper, we propose an area-efficient design of variable-length FFT processor which can perform various FFT lengths of 512/1,024/2,048/4,096/8,192 points used in OFDM-based communication systems, such as digital audio broadcasting (DAB), digital video broadcasting-terrestrial (DVB-T) and digital video broadcasting-handheld (DVB-H). To reduce computational complexity and chip area, we develop a new variable-length FFT architecture by devising a mixed-radix algorithm that consist of radix-2, radix-2² and radix-2/4/8 algorithms and optimizing the realization by substructure sharing. Based on this architecture, an area-efficient design of variable-length FFT processor is presented. By synthesized using the UMC 0.18 μm process, the area of the processor is 2.9 mm² and the 8,192-point FFT can be performed correctly up to 50 MHz with power consumption 823 mW under a 1.8 V supply voltage.

Mixed-radix,virtually scaling-free CORDIC algorithm based rotator for DSP applications

In this work, we proposed a novel Coordinate Rotation DIgital Computer (CORDIC) rotator algorithm that converges faster by performing radix-2,4 and 16 CORDIC iterations while maintaining the scale factor implicitly constant. A mixed-radix is used to achieve convergence faster to reduce the computational latency of the CORDIC algorithm. The main concern of the higher radix CORDIC algorithm is the compensation of a variable scale factor. To solve this problem, the Taylor series approximation of sine and cosine is proposed for a higher radix CORDIC algorithm to achieve the scaling-free rotation of the two-dimensional vector. The scaling-free rotation of the proposed CORDIC algorithm removes the read-only memory (ROM) needed to store scale factor of higher radix CORDIC algorithm. Further, the proposed CORDIC algorithm is designed in rotation mode and optimized by removing the Z datapath for the digital signal processing (DSP) applications for which the angle of rotation is known in advance. Finally, the multipath delay commutator (MDC) fast Fourier transform (FFT) algorithm is implemented with the proposed CORDIC algorithm based rotator on FPGA. The proposed design is compared with existing designs. In a comparison between the radix-16 CORDIC rotator based FFT implementation and our proposed implementation, it has been found out that implementation proposed in this article has used 17% fewer resources.     

Cost-Effective Triple-Mode Reconfigurable Pipeline FFT/IFFT/2-D DCT Processor

This investigation proposes a novel radix-4² algorithm with the low computational complexity of a radix-16 algorithm but the lower hardware requirement of a radix-4 algorithm. The proposed pipeline radix-4² single delay feedback path (R4²SDF) architecture adopts a multiplierless radix-4 butterfly structure, based on the specific linear mapping of common factor algorithm (CFA), to support both 256-point fast Fourier transform/inverse fast Fourier transform (FFT/IFFT) and 8times8 2D discrete cosine transform (DCT) modes following with the high efficient feedback shift registers architecture. The segment shift register (SSR) and overturn shift register (OSR) structure are adopted to minimize the register cost for the input re-ordering and post computation operations in the 8times8 2D DCT mode, respectively. Moreover, the retrenched constant multiplier and eight-folded complex multiplier structures are adopted to decrease the multiplier cost and the coefficient ROM size with the complex conjugate symmetry rule and subexpression elimination technology. To further decrease the chip cost, a finite wordlength analysis is provided to indicate that the proposed architecture only requires a 13-bit internal wordlength to achieve 40-dB signal-to-noise ratio (SNR) performance in 256-point FFT/IFFT modes and high digital video (DV) compression quality in 8 times 8 2D DCT mode. The comprehensive comparison results indicate that the proposed cost effective reconfigurable design has the smallest hardware requirement and largest hardware utilization among the tested architectures for the FFT/IFFT computation, and thus has the highest cost efficiency. The derivation and chip implementation results show that the proposed pipeline 256-point FFT/IFFT/2D DCT triple-mode chip consumes 22.37 mW at 100 MHz at 1.2-V supply voltage in TSMC 0.13-mum CMOS process, which is very appropriate for the RSoCs IP of next-generation handheld devices.     

Low-Power Application-Specific Processor for FFT Computations

In this paper, a processor architecture tailored for radix-4 and mixed-radix FFT computations is described. The processor has native support for power-of-two transform sizes. Several optimizations have been used to improve the energy-efficiency of the processor and experiments show that a programmable solution can possess energy-efficiency comparable to fixed-function ASICs.     

流水线结构FFT/IFFT处理器的设计与实现

针对实时高速信号处理的要求，设计并实现了一种高效的FFT处理器。在分析了FFT算法的复杂度和硬件实现结构的基础上，处理器采用了按频率抽取的基—4算法，分级流水线以及定点运算结构。可以根据要求设置成4P点的FFT或IFFT。处理器可以对多个输入序列进行连续的FFT运算，消除了数据的输入输出对延时的影响。平均每完成一次N点FFT运算仅需要Ⅳ个时钟周期。整个设计基于Verilog HDL语言进行模块化设计。并在Altera公司的Cyclone Ⅱ器件上实现。     

Fixed-point error analysis of radix-4 FHT algorithm with optimisedscaling schemes

The fixed-point error performance of the various fast Hartley transform (FHT) algorithms have been investigated. Scaling schemes have been proposed for each of the algorithms. However, due to their better error performance, only the decimation-in-time (DIT) FHT algorithms have been examined. The fixed-point error analysis of the radix-4 DIT algorithm is discussed first and is shown to agree closely with the simulation results. These results are then compared with the simulation results for radix-2 and split-radix algorithms. The scaling schemes are then optimised and the simulation results of the three algorithms are compared. It is concluded that the radix-4 DIT algorithm has the best error performance     

WFTA算法的FPGA设计与实现

Winograd傅里叶变换算法（WFTA）利用旋转因子W的特性对其进行分解,能够把FFT运算中乘法次数降到最低,是一种高效且资源占用相对较少的FFT实现方法。以256点分解为两维16×16点的小数组WFTA进行运算为例介绍了大数组WFTA算法的FPGA设计与实现方案。仿真测试表明,所设计的256点FFT处理器,乘法器资源消耗仅为基-2FFT的1/2、基-4FFT的2/3,且在100 MHz主时钟频率下完成运算仅需5.8μs,满足FFT处理器的高速实时性要求。     

Designing Fast Fourier Transform Accelerators for Orthogonal Frequency-Division Multiplexing Systems

Designing accelerators for the real-time computation of Fast Fourier Transform (FFT) algorithms for state-of-the-art Orthogonal Frequency-Division Multiplexing (OFDM) demodulators has always been challenging. We have scaled-up a template-based Coarse-Grain Reconfigurable Array device for faster FFT processing that generates special purpose accelerators based on the user input. Using a basic and a scaled-up version, we have generated a radix-4 and mixed-radix (2, 4) FFT accelerator to process different length and types of algorithms. Our implementation results show that these accelerators satisfy not only the execution time requirements of FFT processing for Single Input Single Output (SISO) wireless standards that are IEEE-802.11 a/g and 3GPP-LTE but also for Multiple Input Multiple Output (MIMO) IEEE-802.11n standard.