Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
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08 Feb 2001TL;DR: In this article, two A/D converters (3a, 3b) sample received base band signal Sb by asynchronous sampling clock at double speed of roughly double symbol rate, based on the sampled data series I i, Q i.
Abstract: Two A/D converters (3a, 3b) sample received base band
signal Sb by asynchronous sampling clock at double speed of
symbol rate, and based on the sampled data series I i , Q i .
A transmission complex symbol frequency generator (5)
generates data series E i , D i of transmission complex symbol
frequency component. A correlation value calculator (10)
outputs correlation data series SM i as the correlation value
of cosine wave data series C i , and data series E i , D i of symbol
frequency generated by a cosine wave generator (9), based
on the asynchronous sampling clock CK. An inverse tangent
calculator (11) outputs timing error τ based on the
correlation data series SM i .
5 citations
TL;DR: The problem of finding the asymptotics of trigonometric series in several variables with the terms, having a form of "one minus the cosine" accurate to a decreasing power factor, was exhaustively studied by various authors in a series of publications dating back to the work of G.H. Hardy as mentioned in this paper.
Abstract: The investigation of the asymptotic behavior of trigonometric series near the origin is a prominent topic in mathematical analysis. For trigonometric series in one variable, this problem was exhaustively studied by various authors in a series of publications dating back to the work of G.H. Hardy, 1928. Trigonometric series in several variables have got less attention. The aim of the work is to find the asymptotics of trigonometric series in several variables with the terms, having a form of “one minus the cosine” accurate to a decreasing power factor.
5 citations
5 citations
ENEA1
TL;DR: In this paper, the generalized trigonometric functions are applied to problems in classical mechanics and to the theory of integral equations, and they make further progress in the generalization process by discussing the properties of Laguerre trigonometries along with the relevant link with the Bessel functions.
Abstract: We present some applications of the generalized trigonometric functions to problems in classical mechanics and to the theory of integral equations. We discuss how second and third order trigonometries are ideally suited tools to treat either damped harmonic oscillators and three dimensional rotational models. We make further progress in the generalization process by discussing the properties of Laguerre trigonometries along with the relevant link with the theory of Bessel functions.
5 citations
14 May 1989
TL;DR: It is demonstrated that inverse kinematic solutions can be described by two-dimensional vector rotations and arc tangent operations and that these operations can be efficiently computed by the coordinate rotation digital computer (CORDIC) algorithms.
Abstract: The authors present an LSI (large-scale integrated) circuit for high-speed inverse kinematics computation. They demonstrate that inverse kinematic solutions can be described by two-dimensional vector rotations and arc tangent operations and that these operations can be efficiently computed by the coordinate rotation digital computer (CORDIC) algorithms. The chip is fabricated using 1.5- mu m CMOS gate array technology, and the design of the arithmetic unit on the chip is based on the CORDIC algorithms. Pipelining is fully used in the processor to enhance the operating ration up to 100%. The resulting compact inverse kinematics processor is composed of the above chip and a few memory chips for program and data. The processor can be used for various kinds of manipulators. >
5 citations