Interval sine and cosine functions computation based on variable-precision CORDIC algorithm

2003 ◽  
Author(s):  
J. Hormigo ◽  
J. Villalba ◽  
E.L. Zapata
Keyword(s):  
Cordic Algorithm ◽  
Variable Precision ◽  
Sine And Cosine Functions ◽  
Cosine Functions

The Design and Verification of VGA Controller

2014 ◽  
Vol 981 ◽  
pp. 82-85
Author(s):  
Bin Yu ◽  
Yang Guang
Keyword(s):  
Hardware Implementation ◽  
Cordic Algorithm ◽  
Output Data ◽  
Simple Addition ◽  
Input And Output ◽  
Entire Structure ◽  
Hardware Implementations ◽  
Simulation Results ◽  
Sine And Cosine Functions ◽  
Cosine Functions

CORDIC Algorithm is widely applicable to the hardware implementation of DSP, and it attaches a great importance in many hardware implementations of DSP for a lot of arithmetic operations are simplified to simple addition operations and shifting operations. The FPGA implement of sine and cosine functions are achieved through CORDIC Algorithm in the paper, and the input and output data of the entire structure complies with IEEE754 standards. The basic theory of CORDIC Algorithm is introduced first in the paper, then the hardware iterative formula and the flow chart get out of basic formulas are given, and the structure of the design is introduced in detail, at last synthesis and simulation results are given.

The Implementation of Single Precision Sin&Cos Function on FPGA Based on the CORDIC Algorithm

2013 ◽  
Vol 380-384 ◽  
pp. 1812-1815
Author(s):  
Bin Yu ◽  
Yang Guang ◽  
Hai Huang
Keyword(s):  
Hardware Implementation ◽  
Cordic Algorithm ◽  
Single Precision ◽  
Output Data ◽  
Simple Addition ◽  
Input And Output ◽  
Entire Structure ◽  
Hardware Implementations ◽  
Sine And Cosine Functions ◽  
Cosine Functions

CORDIC Algorithm is widely applicable to the hardware implementation of DSP, and it attaches a great importance in many hardware implementations of DSP for a lot of arithmetic operations are simplified to simple addition operations and shifting operations. The FPGA implement of sine and cosine functions are achieved through CORDIC Algorithm in the paper, and the input and output data of the entire structure complies with IEEE754 standards. The basic theory of CORDIC Algorithm is introduced first in the paper, then the hardware iterative formula and the flow chart get out of basic formulas are given, and the structure of the design is introduced in detail, at last synthesis and simulation results are given.

Some Mellin-type Definite Integrals Involving Sine and Cosine Functions

2019 ◽  
Vol 10 (1) ◽  
pp. 222-237
Author(s):  
M. I. Qureshi ◽  
Kaleem A. Quraishi ◽  
Dilshad Ahamad
Keyword(s):  
Definite Integrals ◽  
Sine And Cosine Functions ◽  
Cosine Functions

SINS Installation Error Calibration Based on Multi-Position Combinations

2011 ◽  
Vol 383-390 ◽  
pp. 4213-4220
Author(s):  
Zhen Huan Wang ◽  
Xi Jun Chen ◽  
Qing Shuang Zeng
Keyword(s):  
Theoretical Analysis ◽  
Least Squares ◽  
Rotation Rate ◽  
Scale Factor ◽  
New Method ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Error Calibration ◽  
Sine And Cosine Functions ◽  
Cosine Functions

A new method is proposed to calibrate the installation errors of SINS. According to the method, the installation errors of the gyro and accelerometer can be calibrated simultaneously, which not depend on latitude, gravity, scale factor and earth's rotation rate. By the multi-position combinations, the installation errors of the gyro and accelerometer are modulated into the sine and cosine functions, which can be identified respectively based on the least squares. In order to verify the correctness of the theoretical analysis, the SINS is experimented by a three-axis turntable, and the installation errors of the gyro and accelerometer are identified respectively according to the proposed method. After the compensation of the installation error, the accuracy of the SINS is improved significantly.

Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution

2020 ◽  
pp. 1-23 ◽  
Author(s):  
T. Sathiyaraj ◽  
JinRong Wang ◽  
D. O'Regan
Keyword(s):  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Second Order ◽  
Delay Systems ◽  
Stochastic Delay ◽  
Finite Dimensional ◽  
Sine And Cosine Functions ◽  
Cosine Functions ◽  
Theoretical Results

Abstract In this paper, we study the controllability of second-order nonlinear stochastic delay systems driven by the Rosenblatt distributions in finite dimensional spaces. A set of sufficient conditions are established for controllability of nonlinear stochastic delay systems using fixed point theory, delayed sine and cosine matrices and delayed Grammian matrices. Furthermore, controllability results for second-order stochastic delay systems driven by Rosenblatt distributions via the representation of solution by delayed sine and cosine functions are presented. Finally, our theoretical results are illustrated through numerical simulation.

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