Showing papers on "Inverse trigonometric functions published in 1993"
TL;DR: A high-speed multifunction chip for performing one of four nonlinear operations: 1) square root, 2) reciprocal, 3) sine/cosine, and 4) arctangent, which signifies an estimated three-to-four-fold increase in speed (for comparable technologies and minimum feature size) over existing approaches.
Abstract: Presents a high-speed multifunction chip for performing one of four nonlinear operations: 1) square root, 2) reciprocal, 3) sine/cosine, and 4) arctangent. Each of these functions is evaluated with one ROM access, two additions, and one major and one minor multiplication, yielding a new result every two clock cycles. Its performance signifies an estimated three-to-four-fold increase in speed (for comparable technologies and minimum feature size) over existing approaches. Furthermore, since all four functions are performed on the same cell, a silicon-area advantage of approximately three is realized when the application demands multiple functions. In wafer scale integration (WSI) of signal and image processing algorithms, several such functions are usually needed, while defect tolerance dictates the use of just one or two types of cells. Thus the new component is ideally suited for monolithic WSI. However, it can also be used as a co-processor/accelerator for commercial DSP chips in hybrid WSI implementation of signal processing algorithms. The underlying principle, which has made the combined goals of high-speed and multifunctionality possible, is second-order interpolation of very small ROM tables. Two versions are presented: a 24-b chip, and a 16-b chip, both fabricated in 2.0- mu m CMOS technology. >
44 citations
Patent•
01 Jul 1993
TL;DR: In this paper, the authors used trigonometric identities to compute the location of the zero, which is very precise, but requires the use of an inverse trigonometric function.
Abstract: The technique to measure the frequency very accurately for electronic warfare (EW) applications, and is simple in hardware, and which can accomplish this goal with a signal with real data (in contrast to complex data). It uses trigonometric identities to compute the location of the zero, which is very precise, but requires the use of an inverse trigonometric function. From these crossings, one can find the frequency very accurately using only one channel of data. The input signal is down converted and digitized with one A/D converter. The digitized data is used to find the zero crossing. The resolution of the zero crossing is limited by the clock cycle. Three uniformly digitized points around a zero crossing are used to find the time for the crossing. The device according to the invention will calculate the frequency very accurately using only one channel of data. This method can be used to measure the angle of arrival in a two antenna configuration with very precise results where the distance between the two antennas does not exceed half the wavelength of the incoming signal.
27 citations
18 citations
TL;DR: It is suggested that any measurement of a trigonometric variable needs necessarily a joint measurement of the two cosine-sine phase quadratures and can be defined in general terms in the framework of quantum estimation theory.
Abstract: The quantum measurement of trigonometric variables is revisted. We show that the probability distributions of the sine and cosine operators of Susskind and Glogower [Physics 1, 49 (1964)] suffer unphysical features for nonclassical states. We suggest that any measurement of a trigonometric variable needs necessarily a joint measurement of the two cosine-sine phase quadratures. In this way unphysical quantum statistics are avoided, and no violation of the trigonometric calculus occurs for expected values. We show that this trigonometric measurement can be defined in general terms in the framework of quantum estimation theory.
14 citations
TL;DR: General error bounds for approximation by quasiinterpolation on ann-cube are developed and an O(ω(f, [-1,1]2,h) error bound for approximation is developed by thin-plate splines supplemented with eight arctan functions.
Abstract: Quasi-interpolation is one method of generating approximations from a space of translates of dilates of a single function ψ. This method has been applied widely to approximation by radial basis functions. However, such analysis has most often been performed in the setting of an infinite uniform grid of centers. In this paper we develop general error bounds for approximation by quasiinterpolation on ann-cube. The quasi-interpolant analyzed involves a finite number, growing ash
−n
, of translates of dilates of the function ψ, and a bounded number of edge functions. The centers of the translates of dilates of ψ form a uniformly spaced grid within the cube. These error bounds are then applied to approximation by thin-plate splines on a square. The result is an O(ω(f, [-1,1]2,h)) error bound for approximation by thin-plate splines supplemented with eight arctan functions.
14 citations
Patent•
23 Jul 1993
TL;DR: In this article, a discrete cosine transformation (DCT) processing device with a small amount of hardware is presented, where the data selecting method in selecting circuits and selection of addition or subtraction in adder/subtractors are switched four times to calculate eight cosine transform coefficients.
Abstract: PURPOSE:To perform the fast discrete cosine transformation(DCT) processing with a small amount of hardware CONSTITUTION:The discrete cosine transformation processing device which obtains a discrete cosine transformation coefficient and an inverse cosine transformation efficient from prescribed input data is provided with 8 independent selecting circuits 140 to 147 which select one data from 8 input data a0 to a7 as a select signal, 7 coefficient multipliers 150 to 156 which are connected to outputs of selecting circuits and multiply select signals b0 to b7 by coefficient P1 to P7 different from one another, and 5 adder/subtractors 161 to 165 which add and substract the outputs of coefficient multipliers in various combinations Adder/subtractors 161 to 163 out of these 5 adder/substractors are used for cosine transform, and the other adder/subtractors 164 and 165 are used for inverse transformation, and the data selecting method in selecting circuits and selection of addition or subtraction in adder/subtractors are switched four times to calculate eight cosine transformation coefficients
4 citations
Patent•
20 Aug 1993
TL;DR: In this paper, a phase change detection method was proposed to attain high speed bit synchronization by detecting a change in a phase of a BPSK or a QPSK and to realize stable burst demodulation with a shorter preamble through inverse modulation pattern synchronization.
Abstract: PURPOSE:To attain high speed bit synchronization by detecting a change in a phase of a pi/2 shift BPSK or a pi/4 shift QPSK preamble and to realize stable burst demodulation with a shorter preamble through inverse modulation pattern synchronization. CONSTITUTION:A phase change detection means 3 extracts a 1/2 bit frequency component by using an alternate data modulation preamble of a pi/2 shift BPSK or a pi/4 shift QPSK. A multiplier means 5 takes correlation with a reference signal and averages the result, and an inverse tangent calculation means 7 obtains a bit timing. A signal point is sampled or interpolated by a value doubling an output of the inverse tangent calculation means 7. Moreover, an output of the inverse tangent calculation means 7 is used, an inverse modulation pattern synchronization means 10 extracts synchronization information of an inverse modulation pattern and the preamble is inversely modulated by using the synchronization pattern. Carrier recovery and phase demodulation are implemented by using a non-modulation signal subject to inverse modulation.
3 citations
Book•
01 Aug 1993
TL;DR: The Real Number System as discussed by the authors is an algebraic concept and operations of Equations and Graphs, and it can be used for building design, as well as for many other applications in geometry.
Abstract: The Real Number System. Algebraic Concepts and Operations of Equations. Geometry. Project 1: Building Design. Functions and Graphs. An Introduction to Trigonometry and Variation. Project 2: Chip Away. Systems of Linear Equations and Determinants. Factoring and Algebraic Fractions. Vectors and Trigonometric Functions. Project 3: Roll ?Em. Fractional and Quadratic Equations. Graphs of Trigonometric Functions. Project 4: Range Finder. Exponents and Radicals. Exponential and Logarithmic Functions. Statistics and Empirical Methods. Project 5: Do You Want . An Introduction to Plane Analytic Geometry. Project 6: Bending Beams. Higher Degree Equations. Systems of Equations and Inequalities. Matrices. Project 7: Shaping Up. Sequences, Series, and the Binomial Formula. Trigonometric Formulas, Identities, and Equations. Project 8: Roller Coaster. An Introduction to Calculus. The Derivative. Applications of Derivatives. Project 9: Fill It Up! Integration. Applications of Integration. Derivatives of Transcendental Functions. Techniques of Integration. Parametric Equations, Vectors, and Polar Coordinates. Partial Derivatives and Multiple Integrals. Infinite Series. First-Order Differential Equations. Second-Order Differential Equations. Numerical Methods and Laplace Transforms. The Metric System. Table of Integrals. Index.
2 citations
01 Jan 1993
TL;DR: In this paper, the inverse of a function y = f (x ) is defined as the function x = g (y ) whose rule un-does what the rule for f does.
Abstract: This chapter discusses inverse functions and their derivatives. The inverse of a function y = f ( x ) is the function x = g ( y ) whose rule un-does what the rule for f does. It is sometimes easier to compute the derivative of the inverse function and invert for the derivative of the function itself. Also, the inverse function rule can be used numerically even when the formula for the inverse function is not known. However, some functions do not have expressions for their inverses. The chapter discusses the microscopic approximation to the inverse and the existence of a limit.
1 citations
01 Jan 1993
TL;DR: Maple contains dozens of predefined commands for representing values of well-known (and lesser-known) mathematical functions at particular points Among these are included such functions as sin x, arctan x,exp x, the error function, and the sine integral as discussed by the authors.
Abstract: Maple contains dozens of predefined commands for representing values of well-known (and lesser-known) mathematical functions at particular points Among these are included such functions as sin x,arctan x,exp x,the error function, and the sine integral
1 citations
TL;DR: A method of straightforward conversion of sinusoidal frequency to Gray code expression using the majority decision principle and threshold logic and a maximum likelihood estimator is described.
Abstract: A method of straightforward conversion of sinusoidal frequency to Gray code expression is described. The unknown frequency is estimated using only the sign of the inverse cosine function. The frequency conversion error is shown by computer experiment. For a more accurate result, the majority decision principle and threshold logic, that is, a maximum likelihood estimator, are applied. Hardware implementation is so easy that the whole system can be implemented on an LSI chip.