Improved Scaling-Free CORDIC algorithm

Moroz, Leonid; Mykytiv, Taras; Herasym, Martyn

doi:10.1109/ewdts.2013.6673174

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…However, due to the high number of iterations and the high computational delay, it is only suitable for applications with low requirements for real-time performance [48]. In hyperbolic coordinates, assuming that after the i-th rotation, the vector (x i , y i ) rotated by an angle α i yields the vector (x i+1 , y i+1 ), the corresponding relationship between the two coordinates is as follows [49,50]:…”

Section: Dynamic Range Transformation Module Based On the Improved Sc...mentioning

confidence: 99%

The Ultrasound Signal Processing Based on High-Performance CORDIC Algorithm and Radial Artery Imaging Implementation

et al. 2023

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The radial artery reflects the largest amount of physiological and pathological information about the human body. However, ultrasound signal processing involves a large number of complex functions, and traditional digital signal processing can hardly meet the requirements of real-time processing of ultrasound data. The research aims to improve computational accuracy and reduce the hardware complexity of ultrasound signal processing systems. Firstly, this paper proposes to apply the coordinate rotation digital computer (CORDIC) algorithm to the whole radial artery ultrasound signal processing, combines the signal processing characteristics of each sub-module, and designs the dynamic filtering module based on the radix-4 CORDIC algorithm, the quadrature demodulation module based on the partitioned-hybrid CORDIC algorithm, and the dynamic range transformation module based on the improved scale-free CORDIC algorithm. A digital radial artery ultrasound imaging system was then built to verify the accuracy of the three sub-modules. The simulation results show that the use of the high-performance CORDIC algorithm can improve the accuracy of data processing. This provides a new idea for the real-time processing of ultrasound signals. Finally, radial artery ultrasound data were collected from 20 volunteers using different probe scanning modes at three reference positions. The vessel diameter measurements were averaged to verify the reliability of the CORDIC algorithm for radial artery ultrasound imaging, which has practical application value for computer-aided clinical diagnosis.

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Section: Dynamic Range Transformation Module Based On the Improved Sc...mentioning

confidence: 99%

The Ultrasound Signal Processing Based on High-Performance CORDIC Algorithm and Radial Artery Imaging Implementation

et al. 2023

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“…Nevertheless, the computation and correction of variable scale factor was a focused issue for higher radix CORDIC algorithms [ 26 , 27 , 28 , 29 ] and advanced hybrid CORDIC algorithms [ 30 ]. The scale-free CORDIC algorithm [ 31 , 32 ] approximated the sine and cosine functions by the Taylor series, thereby eliminating the need for the scalar factors, except for a limited convergence range and poor accuracy. A new hybrid CORDIC algorithm was proposed [ 33 ] to be able to further reduce the latency of CORDIC by reducing the number of iterations equal to (3 N /8) + 1.…”

Section: Related Workmentioning

confidence: 99%

A Low-Latency RDP-CORDIC Algorithm for Real-Time Signal Processing of Edge Computing Devices in Smart Grid Cyber-Physical Systems

Qin

Liu

Hou

et al. 2022

Sensors

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Smart grids are being expanded in scale with the increasing complexity of the equipment. Edge computing is gradually replacing conventional cloud computing due to its low latency, low power consumption, and high reliability. The CORDIC algorithm has the characteristics of high-speed real-time processing and is very suitable for hardware accelerators in edge computing devices. The iterative calculation method of the CORDIC algorithm yet leads to problems such as complex structure and high consumption of hardware resource. In this paper, we propose an RDP-CORDIC algorithm which pre-computes all micro-rotation directions and transforms the conventional single-stage iterative structure into a three-stage and multi-stage combined iterative structure, thereby enabling it to solve the problems of the conventional CORDIC algorithm with many iterations and high consumption. An accuracy compensation algorithm for the direction prediction constant is also proposed to solve the problem of high ROM consumption in the high precision implementation of the RDP-CORDIC algorithm. The experimental results showed that the RDP-CORDIC algorithm had faster computation speed and lower resource consumption with higher guaranteed accuracy than other CORDIC algorithms. Therefore, the RDP-CORDIC algorithm proposed in this paper may effectively increase computation performance while reducing the power and resource consumption of edge computing devices in smart grid systems.

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“…The combination of the memory units, iterative scaling-free CORDIC algorithms, and multipliers provides a method without deformation module of the vector, which significantly saves hardware resources in FPGA implementation and reduces delays. The theoretical basis for the proposed method and its 16-bit microcontroller implementation are described in [11,14]. However, no hardware implementation on FPGA has been reported until now.…”

Section: General Approachmentioning

confidence: 99%

“…The scale factor for conventional CORDIC is √ 1 + 2 −2 and for the scaling-free CORDIC it is √ 1 + 2 −4 −2 on every iteration . An angle = 2 − is also updated by the values arctan and arctan[(2 )/(2 − 2 )] accordingly [11,14]. For a given value , influence of the scale factor on the results of calculations for the conventional CORDICs is canceled when 4], and for the scaling-free CORDIC it is canceled when √ 1 + 2 −4 −2 − 1 < Δ , beginning from [11] modul sf ≥ ⌈ − 3 4 ⌉ .…”

Section: Proposed Algorithmmentioning

confidence: 99%

Simple Hybrid Scaling-Free CORDIC Solution for FPGAs

Moroz

Nagayama

Mykytiv

et al. 2014

International Journal of Reconfigurable Computing

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COordinate Rotation DIgital Computer (CORDIC) is an effective method that is used in digital signal processing applications for computing various trigonometric, hyperbolic, linear, and transcendental functions. This paper presents the theoretical basis and practical implementation of circular (sine-cosine) CORDIC-based generator. Synthesis results of this generator based on Altera Stratix III FPGA (EP3SL340F1517C2) using Quartus II version 9.0 show that the proposed hybrid FPGA architecture significantly reduces latency (42% reduction) with a small area overhead, compared to the conventional version. The proposed algorithm has been simulated for sine and cosine function evaluation, and it has been verified that the accuracy is comparable with conventional algorithm.

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Improved Scaling-Free CORDIC algorithm

Cited by 3 publications

References 2 publications

The Ultrasound Signal Processing Based on High-Performance CORDIC Algorithm and Radial Artery Imaging Implementation

The Ultrasound Signal Processing Based on High-Performance CORDIC Algorithm and Radial Artery Imaging Implementation

A Low-Latency RDP-CORDIC Algorithm for Real-Time Signal Processing of Edge Computing Devices in Smart Grid Cyber-Physical Systems

Simple Hybrid Scaling-Free CORDIC Solution for FPGAs

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