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DCT Architectures
Published in Keshab K. Parhi, Takao Nishitani, Digital Signal Processing for Multimedia Systems, 2018
CORDIC (COrdinate Rotation Digital Computer) is a technique commonly used to compute trigonometric functions in low-cost hardware [50, 67]. Rotation is a basic computation realizable by CORDIC. Given x, y, and θ, −π/2 < θ < π/2, the CORDIC algorithm, in its rotation mode, computes () [x′y′]=K⋅[cosθ−sinθsinθcosθ]⋅[xy],
C
Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
coordinated rotation digital computer (CORDIC) coordinated rotation digital computer (CORDIC) algorithm for calculating trigonometric functions using only additions and shift operations. coordinating unit See coordinator unit. performs either iterative or periodic coordination of the local decisions; coordinator unit is often regarded as the supremal unit of the hierarchical control structure. Also called coordinating unit. copolarized the plane wave whose polarization is the same as that of the reference plane wave (e.g., radiated wave from an antenna) is said to be copolarized (otherwise it is crosspolarized). copper jacket timer a magnetic time-off timer that can be used in definite time DC motor acceleration starters and controllers. The copper jacket relay functions by slowing the dissipation of the magnetic field when the coil is turned off. After a certain amount of time the spring tension on the contactor overcomes the strength of the dissipating magnetic field -- and causes the contacts to change state. Time delays with the copper jacket timer are adjusted by adding, or removing, permeable shims between the coil and copper jacket. The more shims in place the slower the magnetic field dissipates, hence the longer the time delay becomes. copper loss electric loss due to the resistance in conductors, windings, brush contacts or joints, in electric machinery or circuits. Also referred to as I 2 R, the losses are manifested as heat. coprime 2-D polynomial matrices See coprimeness of 2-D polynomial matrices. coprime 2-D polynomials 2-D polynomials. See coprimeness of
Arithmetic and Logical Programming
Published in A. Arockia Bazil Raj, FPGA-Based Embedded System Developer's Guide, 2018
Most engineers and scientists aim to implement trigonometric functions such as sine, cosine, tan, cosecant, secant, and cot in FPGA, which they initially thought of accomplishing by means of a lookup table, possibly combined with linear interpolation or a power series if multipliers are available. The CORDIC algorithm is one of the most important, and a simple one was designed to calculate trigonometric functions just by rotation and additions. This algorithm was invented by Jack Volder in 1959 while designing a new navigation computer [39,44,45]. The real beauty of this algorithm is that we can implement it with a very small FPGA footprint because we require only a shifter and adder. The CORDIC requires only a small lookup table, along with the logic to perform shift and add operations. Importantly, the algorithm requires no dedicated multipliers or dividers. This algorithm is one of the most important for many modern scientific applications. For example, designers use CORDIC in many controllers to implement mathematical transfer functions, true RMS measurement, signal processing, image processing, and biomedical applications. The CORDIC algorithm can operate in one of three configurations: linear, circular, or hyperbolic [39,45]. Within each of these configurations, the algorithm functions in one of two modes: rotation or vectoring. In rotation mode, the input vector is rotated by a specified angle, whereas in vectoring mode, the algorithm rotates the input vector to the x axis while recording the angle of rotation required.
Implementation of FPGA design of FFT architecture based on CORDIC algorithm
Published in International Journal of Electronics, 2021
Sharath Chandra Inguva, J.B. Seventiline
The CORDIC is an algorithm for the calculation of rotation angle in digital system by the shift-add operation (Luo et al., 2018). It was derived by Jack E. Volder (Biswas& Maharatna, 2015) in 1959 from the basic equation of the vector rotation. The main principle of CORDIC algorithm is simple which divide the rotation angle in micro-rotation angles series. This algorithm is used in many applications such as cosine and sine functions generation, household transform, discrete sine/cosine transforms (DST/DCT), fast Fourier transforms (FFT), etc. (Li et al., 2019). This algorithm is used in VLSI implementation because of the simple operations and it performs several operations such as addition, bit-shift and subtraction. It is used for the calculation of trigonometric functions, divisions, multiplications and other complex functions. In signal processing and elementary function evaluation, CORDIC algorithm works more effectively (Heidarpour et al., 2016; Ramadoss et al., 2017). The power consumption and the convergence of linear-rate are the main issue in conventional CORDIC algorithm (Weißbrich et al., 2019) with the speed of iterations and the source of word-length. By the array of shifts-add operations, the overall performance is affected (J. Chen et al., 2016; Nawandar et al., 2016).
An elementary algorithm to evaluate trigonometric functions to high precision
Published in International Journal of Mathematical Education in Science and Technology, 2018
A student learning trigonometry might ponder on the question how values of the basic trigonometric functions like cos θ are actually evaluated. Typically, a calculator (or computer) is at hands when having to find a particular value. We recall the rather simple geometric idea behind a common method implemented in calculators and computers for evaluating trigonometric functions namely the Cordic algorithm [1]. We shall see that with an additional idea from computer science, termed arbitrary-precision arithmetic (or ‘bignum’ arithmetic), a basic version of Cordic can be used to generate values of the cosine function to hundreds of correct decimal places. To keep the presentation elementary, to be useful for a beginner of trigonometry, we focus solely on the evaluation of cosine; at the end, we point to some references on how other elementary functions can be similarly evaluated.
A unified reconfigurable CORDIC processor for floating-point arithmetic
Published in International Journal of Electronics, 2020
Linlin Fang, Bingyi Li, Yizhuang Xie, He Chen, Long Pang
The CORDIC algorithm involves a simple shift-and-add iterative procedure to perform several computing tasks. It can execute the rotation of a two-dimensional (2D) vector in linear, circular and hyperbolic coordinates systems (Walther, 1971). Due to the simplicity of its hardware implementation, CORDIC has a wide range of applications in signal processing and image processing, such as QR decomposition (Lightbody, Woods, & Walke, 2003), singular value decomposition (Cavallaro & Luk, 1987), 3D graphics (Lang & Antelo, 2005) and robotics (Kameyama, Amada, & Higuchi, 1992). The hardware implementation of these applications requires more than one CORDIC processor operating in different modes and different trajectories.