改进型CORDIC算法的研究与实现

CORDIC的运算速度问题是研究的热点。为了解决CORDIC运算速度慢的问题,采用跳过零点思想,跳过输入相位值中为0的位,有效的减少了迭代次数。利用ISE仿真技术多次仿真综合。验证出改进型的CORDIC算法,在保证算法的运算精度基础上,明显地改善了CORDIC的运算速度,尤其针对于一些特殊的旋转角度,利用极少的旋转就达到结果。最终利用FPGA实现改进后CORDIC算法。     

Modified CORDIC algorithm with reduced iterations

Presents a modified CORDIC algorithm that offers a considerable latency time reduction and chip area savings when compared with the original CORDIC method. The operations used are adds, shifts, and multiplication or division.<>     

字长可重构流水线CORDIC设计

设计了一种数据字长可重构的流水线坐标旋转数字计算(Coord inate R otation D ig ita l Com pu ting,CORD IC)单元,用于可重构DSP阵列式处理引擎的处理单元核心的设计。首先对流水线CORD IC的模校正进行改造,使流水级数有所减少,且使模校正流水的分配有利于字长可重构的设计。之后通过相邻8位流水线CORD IC单元间的横向和纵向可重构设计,使相邻的(2×2)/(3×3)/(4×4)个基本单元可以组合成数据字长为16/24/32位的CORD IC单元。     

Design, Implementation and Analysis of a New Redundant CORDIC Processor with Constant Scaling Factor and Regular Structure

A new high-speed redundant CORDIC processor is designed and implemented based on the double rotation method, which turns out to be the two-dimensional (2D) Householder CORDIC, a special case of the generalized Householder CORDIC in the 2D Euclidean vector space. The new processor has the advantages of regular structure and high throughput rate. The pipelined structure with radix-2 signed-digit (SD) redundant arithmetic is adopted to reduce the carry-propagation delay of the adders while the digit-serial structure alleviates the burden of the hardware cost and I/O requirement. Compared to previously proposed designs, the new CORDIC processor preserves the constant scaling factor, an important merit of the original CORDIC, and thus does not require any complicated division or square-root operations for variable scaling factor calculation. Furthermore, the processor is well suited to VLSI implementation since it does not call for any irregularly inserted correcting iterations. Both angle calculation mode for computing trigonometric function and vector rotation mode for plane rotations are supported. Practical VLSI chip implementation of the fixed-point redundant CORDIC processor using 0.6 m standard cell library is given including detailed numerical error analysis.     

一种基于0.35m工艺的高速混合旋转结构DDFS

设计实现了一种基于CORDIC算法和乘法器的直接数字频率合成器。采用混合旋转算法实现相位幅度转换,最高工作频率达到400MHz。在算法级,将DDFS中需要执行的π/4旋转操作分成两次旋转完成,第一次旋转采用CORDIC算法,第二次旋转采用乘法器来完成,同时采用流水线结构来实现累加器,提高整体性能。在晶体管级,采用DPL(Double-pass-transistor logic)逻辑实现基本电路单元,减少延迟提高速度。经0.35μmCMOS工艺流片,在400MHz的工作频率下,输出信号在80MHz处,SFDR为76.47dB,整个芯片面积为3.4mm×3.8mm。     

A CMOS floating-point vector-arithmetic unit

This work describes a floating-point arithmetic unit based on the CORDIC algorithm. The unit computes a full set of high level arithmetic and elementary functions: multiplication, division, (co)sine, hyperbolic (co)sine, square root, natural logarithm, inverse (hyperbolic) tangent, vector norm, and phase. The chip has been integrated in 1.6 μm double-metal n-well CMOS technology and achieves a normalized peak performance of 220 MFLOPS     

Multilevel barrel shifter for CORDIC design

The coordinate rotation digital computer (CORDIC) algorithm is used in numerous special purpose systems for real-time signal processing applications. It uses barrel shifters to complete shift operations. However, the barrel shifter occupies most of the area of the CORDIC chip. A new structure of multilevel barrel shifters is presented. With this structure the shifter size is reduced by 68%. The novel structure can also slightly reduce the latency time of shift operations     

Ultra Low Power CORDIC Processor for Wireless Communication Algorithms

We designed and implemented an ultra low power CORDIC processor which targets the implementation of advanced wireless communications algorithms based on Givens rotations and Householder reflections. We propose a modified CORDIC algorithm and architecture, and we elaborate on the low power architectural and algorithmic techniques for minimizing its power consumption. Our CORDIC implementation consumes, in rotate mode, on average 50 W @ 10 MHz under 1 V supply voltage in a .25 m technology.     

A 540-MHz 10-b polar-to-Cartesian converter

A 10-b polar-to-Cartesian converter for generating digital sine and cosine waveforms simultaneously with a maximum sample rate of 540 MHz is presented. The converter is derived from a coordinate rotation digital computer (CORDIC) processor. Implementation details and the chip layout are given. The converter is implemented in a 1-μm 13-GHz triple-level interconnect bipolar process, requiring 1000 mW from a single 5-V supply. The die size is 25 mm²     

基于CORDIC算法的NCO设计

NCO有着广泛的应用。本文从基本的坐标变换公式出发,严谨地推导了CORDIC的原理,简明扼要地阐明了“徽旋转”和“模畸变预矫正”。采用流水线CORDIC单元实现了NCO中的FG部分。并对在具体的FPGA上布局布线之后的数据进行了频谱分析,验证了理论的正确性。     

Digit-pipelined direct digital frequency synthesis based on differential CORDIC

A novel direct digital frequency synthesis (DDFS) architecture based on the differential CORDIC (DCORDIC) algorithm is presented. The architecture allows digit-level pipelining in the CORDIC angle path by implementing a two-dimensional systolic array. Unlike other DDFS architectures, it incorporates the phase accumulator in the digit-level pipelining framework so that a bottleneck-free datapath throughout the whole system is achieved in a scalable manner. A generic environment that generates fully synthesizable Verilog codes that implement the proposed architecture is created and the physical attributes of the resulting system are discussed.     

CORDIC algorithm for vectoring mode without constant scalingfactors

A new CORDIC algorithm is presented that can be used for the vectoring mode without requiring constant scaling factors. The algorithm can also be used to carry out complete transformation from rectangular co-ordinates (x,y) to polar co-ordinates (ρ&thetas;) in each iteration. The exponent difference of x and y is computed so as to speed up convergence. This new CORDIC algorithm has an average of 0.75 n iterations for n-bit input data and can achieve>94.78% 23 bit accuracy. It is also suitable for VLSI chip implementation due to the regular architecture required     

一种新型的用于数字信号处理的进化硬件原胞结构

采用CORDIC算法在单一的电路体系结构下实现了具有多种算术功能的进化电路原胞。该原胞可以作为构建此类进化硬件的基本组成模块。分析表明,采用CORDIC算法的原胞具有丰富的运算能力而只消耗较少的芯片资源,可以成为一种有前途的用于数字信号处理功能级进化电路的原胞设计的方案。     

高性能HPOR CORDIC算法及实现

CORDIC算法在通信和图像处理等各个领域有着广泛的应用,但是浮点CORDIC由于迭代延时大且实现复杂没有得到很好的应用,本文提出了一种修正浮点CORDIC算法：高精度顺序迭代HPORCORDIC。该算法以接近定点的运算代价完成浮点运算迭代,运算速度和硬件实现规模与定点CORDIC相当,运算精度与浮点CORDIC相当,克服了定点CORDIC运算精度差,浮点CORDIC迭代延时大、实现复杂的问题。该算法既可用于通用微处理器的设计,也可用于高性能DSP的设计。     

A high-speed halftoning processor for raster scanned images

A high-speed bilevel reproduction algorithm, called modified error diffusion (MED) algorithm, has been developed to provide high-quality halftoning images for continuous tone images and has been implemented in a CMOS LSI chip. The chip has been designed with standard-cell 1.5-μm CMOS technology using an optimum layout design. The chip has achieved a maximum processing speed of 60 ns/pixel     

IS-CORDIC: a fixed-point inverse recoded single iteration CORDIC architecture

This paper presents a novel modified Coordinate Rotation Digital Computer (CORDIC) architecture that computes values of sine and cosine in a single cycle. The proposed method utilises angle-recoding technique to design a modified CORDIC algorithm. Multiple iterations are merged in the modified algorithm using memory storage for initial iterations and employing inverse recoding to generate constant multiplication factors for the remaining iterations. Scale factor of the algorithm remains constant, as these factors are independent of intermediate directions of rotation. In addition, the architecture is mapped onto a single CORDIC computation element that requires only a single cycle to compute the result. These multiplications are implemented using dedicated hardware multipliers in Field Programmable Gate Arrays and customised fixed-point multiplication techniques for Application Specific Integrated Circuits. Implementation results show that the proposed IS-CORDIC architecture is 7.9 times more efficient than basic CORDIC and has reduced area-delay product than current state of the art implementations.     

CORDIC算法的FPGA与DSP实现的优劣分析

介绍了坐标旋转数字计算机（CORDIC）的算法原理,分析了算法中旋转迭代次数、操作数位宽与精度的关系,在现场可编程门阵列（FPGA）芯片和数字信号处理器（DSP）芯片上用全流水、高并行结构分别实现了旋转模式下的CORDIC算法,并将两者的精度、时间效率、空间效率的优劣进行比较。结果表明,DSP数值精度比FPGA高且设计更灵活,可移植性更强;而FPGA速度远远快于DSP,消耗硬件资源更少。     

基于改进CORDIC算法的数字预失真实现

针对传统CRODIC算法存在的角度扩展、迭代复杂度等问题,在旋转模式下提出一种改进型CORDIC算法。对于旋转角度范围的扩展,采取将向量限制在第一和第四象限,旋转最后再根据输入向量符号判断旋转角度值;对于迭代复杂度,采用跳跃旋转方式来减少迭代次数。最后在Quartus软件上实现了该改进算法,并且将改进后的CORDIC算法应用于数字预失真技术,在FPGA上设计实现。仿真与实验结果表明:与传统的CORDIC算法相比,改进算法减少了硬件的开销,运算速度和精度都有很大改进,能够快速提取预失真参数,显著提高功率放大器的线性度。     

A Modified CORDIC FPGA Implementation for Wave Generation

This paper presents a modified coordinate rotation digital computer (CORDIC) algorithm implemented in parallel architecture to generate sine and cosine waveform. Since CORDIC is a combination of only additions and shifts, it can be efficiently implemented in hardware. The proposed algorithm further approximates the way of computing rotation angle based on Taylor series in order to reduce the usage of Read-Only-Memory (ROM) table. Thus area and power is reduced due to partial usage of ROM storage. The precision remains the same as the original algorithm. The modified 32-bits pipeline CORDIC are implemented in Spartan XC3S500E device using Xilinx ISE 12.3 design suite. The result is compared with original CORDIC and Xilinx coregen in device utilization. It is shown that the logic usage is 31 FFs and 285 FFs less than the original design and Xilinx core, respectively. When compared with the original design, the signal power and total power reduction at 40 MHz clocks are 7.69 % and 1.35 %, respectively. The bit error remains at 10^?8 dB level. The SNR of modified CORDIC is about 2 dB lower, which is acceptable in wave generation.     

Configurable Floating-Point FFT Accelerator on FPGA Based Multiple-Rotation CORDIC

Fast Fourier transform (FFT) accelerator and Coordinate rotation digital computer (CORDIC) algorithm play important roles in signal processing.We propose a conflgurable floating-point FFT accelerator based on CORDIC rotation,in which twiddle direction prediction is presented to reduce hardware cost and twiddle angles are generated in real time to save memory.To finish CORDIC rotation efficiently,a novel approach in which segmentedparallel iteration and compress iteration based on CSA are presented and redundant CORDIC is used to reduce the latency of each iteration.To prove the efficiency of our FFT accelerator,four FFT accelerators are prototyped into a FPGA chip to perform a batch-FFT.Experimental results show that our structure,which is composed of four butterfly units and finishes FFT with the size ranging from 64 to 8192 points,occupies 33230(3％) REGs and 143006(30％)LUTs.The clock frequency can reach 122MHz.The resources of double-precision FFT is only about 2.5 times of single-precision while the theoretical value is 4.What's more,only 13331 cycles are required to implement 8192-points double-precision FFT with four butterfly units in parallel.