To overcome the drawbacks such as irregular circuit construction and low system throughput that exist in conventional methods, a new factor correction scheme for coordinate rotation digital computer（ CORDIC） algorit...To overcome the drawbacks such as irregular circuit construction and low system throughput that exist in conventional methods, a new factor correction scheme for coordinate rotation digital computer（ CORDIC） algorithm is proposed. Based on the relationship between the iteration formulae, a new iteration formula is introduced, which leads the correction operation to be several simple shifting and adding operations. As one key part, the effects caused by rounding error are analyzed mathematically and it is concluded that the effects can be degraded by an appropriate selection of coefficients in the iteration formula. The model is then set up in Matlab and coded in Verilog HDL language. The proposed algorithm is also synthesized and verified in field-programmable gate array （FPGA）. The results show that this new scheme requires only one additional clock cycle and there is no change in the elementary iteration for the same precision compared with the conventional algorithm. In addition, the circuit realization is regular and the change in system throughput is very minimal.展开更多
The implementation of the coordinate rotational digital computer （CORDIC） algorithm with wave pipelining technique on field programmable gate array （FPGA） is described. All data in FPGA-based wave pipelining pass ...The implementation of the coordinate rotational digital computer （CORDIC） algorithm with wave pipelining technique on field programmable gate array （FPGA） is described. All data in FPGA-based wave pipelining pass through a number of logic gates, in the same way that all data pass through the same number of registers in a conventional pipeline. Moreover, all paths are routed using identical routing resources. The manual placement, timing driven routing and timing analyzing techniques are applied to optimize the layout for achieving good path balance. Experimental results show that a 256-LUT logic depth circuit mapped on XC4VLX15-12 runs as high as 330 MHz, whichis a little lower than the speed of 336 MHz based on the conventional 16-stage pipelining in the same chip. The latency of the wave pipelining circuit is 30.3 ns, which is 36.4% shorter than the latency of 16-stage conventional pipelining circuit.展开更多
It is an important problem that we implement floating point trigonometric functions of high precision with suitable hardware cost for high performance in digit image processing. The coordinate rotational digital compu...It is an important problem that we implement floating point trigonometric functions of high precision with suitable hardware cost for high performance in digit image processing. The coordinate rotational digital computer （CORDIC） arithmetic to is used to solve the above problem in this paper. In order to increase the speed of operation, it chooses the pipeline architecture. The results are disposed by IEEE-754 standard. The CORDIC architecture is modeled by using the verilog HDL and verified with MATLAB program and ModelSim 6.2SE tool. A 32 bits radix-2 CORDIC architecture was implemented on the available FPGA platform. The entire CORDIC architecture operated at 126.34 MHz of clock rate with a power consumption of 318.56 mW. Its theoretical background, procedures, simulation results and conclusions are presented in this paper.展开更多
本文针对传统坐标旋转数字计算机(Coordinate Rotation Digital Computer,CORDIC)算法存在时延长、资源消耗多等问题,提出一种低时延小容量查找表的新型CORDIC实现方案。通过创新性设计,显著优化了算法的时序性能与硬件资源消耗。该方...本文针对传统坐标旋转数字计算机(Coordinate Rotation Digital Computer,CORDIC)算法存在时延长、资源消耗多等问题,提出一种低时延小容量查找表的新型CORDIC实现方案。通过创新性设计,显著优化了算法的时序性能与硬件资源消耗。该方法摒弃传统迭代运算,仅需要构建小容量ROM表,结合简单位移操作,即可实现高精度三角函数输出。经Matlab理论仿真与ModelSim数字验证,该方法处理延迟压缩至2个时钟周期,并且在资源占有率和精度方面也有显著提升,具有一定的理论与实用价值。展开更多
本文提出了一种基于CORDIC (Coordinate Rotation Digital Computer)算法的数字鉴频方法。首先给出了基于CORDIC算法的鉴相原理,讨论了CORDIC算法的鉴相范围;然后讨论了差分鉴频的方法,特别是对低数据率情况下的差分鉴频进行了探讨,并...本文提出了一种基于CORDIC (Coordinate Rotation Digital Computer)算法的数字鉴频方法。首先给出了基于CORDIC算法的鉴相原理,讨论了CORDIC算法的鉴相范围;然后讨论了差分鉴频的方法,特别是对低数据率情况下的差分鉴频进行了探讨,并给出了一种实用的数字鉴频结构。计算机仿真结果和FPGA仿真结果表明,基于CORDIC算法流水结构和一阶差分结构实现的数字鉴频方法是可行的,而且是高效的。展开更多
针对传统串行坐标旋转数字计算方法(CORDIC)耗时且占用较多资源的缺点,提出了一种旋转模式下CORDIC算法的新型改进算法,该改进算法可用来代替直接数字频率合成器(DDS)查找表进行正余弦的计算。通过采用贪婪算法实现对CORDIC旋转方向与...针对传统串行坐标旋转数字计算方法(CORDIC)耗时且占用较多资源的缺点,提出了一种旋转模式下CORDIC算法的新型改进算法,该改进算法可用来代替直接数字频率合成器(DDS)查找表进行正余弦的计算。通过采用贪婪算法实现对CORDIC旋转方向与旋转角度的优化,从而可以达到串行转并行和减少迭代次数、节约资源的目的。该算法可以应用于三角函数的复杂函数的硬件实现中。仿真结果表明,在迭代次数相同的情况下,改进算法较传统算法可以获得更高的精度。最后,在Xilinx FPGA的Spartan-3E芯片上实现了改进的CORDIC结构。与传统CORDIC算法相比,在运算精度为10-5时,可以节省Slices、LUTs(Look Up Tables)资源分别为28%和25%。展开更多
基金The National High Technology Research and Development Program of China (863 Program)(No.2007AA01Z280)
文摘To overcome the drawbacks such as irregular circuit construction and low system throughput that exist in conventional methods, a new factor correction scheme for coordinate rotation digital computer（ CORDIC） algorithm is proposed. Based on the relationship between the iteration formulae, a new iteration formula is introduced, which leads the correction operation to be several simple shifting and adding operations. As one key part, the effects caused by rounding error are analyzed mathematically and it is concluded that the effects can be degraded by an appropriate selection of coefficients in the iteration formula. The model is then set up in Matlab and coded in Verilog HDL language. The proposed algorithm is also synthesized and verified in field-programmable gate array （FPGA）. The results show that this new scheme requires only one additional clock cycle and there is no change in the elementary iteration for the same precision compared with the conventional algorithm. In addition, the circuit realization is regular and the change in system throughput is very minimal.
文摘The implementation of the coordinate rotational digital computer （CORDIC） algorithm with wave pipelining technique on field programmable gate array （FPGA） is described. All data in FPGA-based wave pipelining pass through a number of logic gates, in the same way that all data pass through the same number of registers in a conventional pipeline. Moreover, all paths are routed using identical routing resources. The manual placement, timing driven routing and timing analyzing techniques are applied to optimize the layout for achieving good path balance. Experimental results show that a 256-LUT logic depth circuit mapped on XC4VLX15-12 runs as high as 330 MHz, whichis a little lower than the speed of 336 MHz based on the conventional 16-stage pipelining in the same chip. The latency of the wave pipelining circuit is 30.3 ns, which is 36.4% shorter than the latency of 16-stage conventional pipelining circuit.
基金supported by the Shanghai AM Foundation(Grant No.09700714000)
文摘It is an important problem that we implement floating point trigonometric functions of high precision with suitable hardware cost for high performance in digit image processing. The coordinate rotational digital computer （CORDIC） arithmetic to is used to solve the above problem in this paper. In order to increase the speed of operation, it chooses the pipeline architecture. The results are disposed by IEEE-754 standard. The CORDIC architecture is modeled by using the verilog HDL and verified with MATLAB program and ModelSim 6.2SE tool. A 32 bits radix-2 CORDIC architecture was implemented on the available FPGA platform. The entire CORDIC architecture operated at 126.34 MHz of clock rate with a power consumption of 318.56 mW. Its theoretical background, procedures, simulation results and conclusions are presented in this paper.
文摘本文针对传统坐标旋转数字计算机(Coordinate Rotation Digital Computer,CORDIC)算法存在时延长、资源消耗多等问题,提出一种低时延小容量查找表的新型CORDIC实现方案。通过创新性设计,显著优化了算法的时序性能与硬件资源消耗。该方法摒弃传统迭代运算,仅需要构建小容量ROM表,结合简单位移操作,即可实现高精度三角函数输出。经Matlab理论仿真与ModelSim数字验证,该方法处理延迟压缩至2个时钟周期,并且在资源占有率和精度方面也有显著提升,具有一定的理论与实用价值。
文摘本文提出了一种基于CORDIC (Coordinate Rotation Digital Computer)算法的数字鉴频方法。首先给出了基于CORDIC算法的鉴相原理,讨论了CORDIC算法的鉴相范围;然后讨论了差分鉴频的方法,特别是对低数据率情况下的差分鉴频进行了探讨,并给出了一种实用的数字鉴频结构。计算机仿真结果和FPGA仿真结果表明,基于CORDIC算法流水结构和一阶差分结构实现的数字鉴频方法是可行的,而且是高效的。
文摘针对传统串行坐标旋转数字计算方法(CORDIC)耗时且占用较多资源的缺点,提出了一种旋转模式下CORDIC算法的新型改进算法,该改进算法可用来代替直接数字频率合成器(DDS)查找表进行正余弦的计算。通过采用贪婪算法实现对CORDIC旋转方向与旋转角度的优化,从而可以达到串行转并行和减少迭代次数、节约资源的目的。该算法可以应用于三角函数的复杂函数的硬件实现中。仿真结果表明,在迭代次数相同的情况下,改进算法较传统算法可以获得更高的精度。最后,在Xilinx FPGA的Spartan-3E芯片上实现了改进的CORDIC结构。与传统CORDIC算法相比,在运算精度为10-5时,可以节省Slices、LUTs(Look Up Tables)资源分别为28%和25%。
