Showing papers on "Inverse trigonometric functions published in 1988"

Effective approximations suitable for the control algorithm of microprocessor-based cycloconvertor

Abstract: Two approximation methods for simplifying the control algorithm of cycloconvertor control are obtained from studies in a phase plane called a 'time process chart'. One is a simple straight line approximation, in which only arithmetic operations are involved, and in the use of trigonometric or inverse trigonometric functions which can be avoided. The other is also a straight line approximation, but some function tables are used in combination, to improve the accuracy of approximation. To evaluate the accuracy, the theoretical output waveform obtained by each of the above approximations is analysed using the DFT method. Results of the analysis show that both approximations can be used effectively for the control algorithm, and that the second method, in particular, is highly accurate. Requiring only simple procedures in application, both of the two proposed methods can be used advantageously for microprocessor-based control. >

Digital chrominance signal processing circuit

Abstract: PURPOSE:To lead out an AFC signal, an APC signal, and an ACC signal at a high speed and to simplify the circuit constitution by subjecting an input color burst signal to prescribed arithmetic. CONSTITUTION:The phase of the color burst signal is shifted at 90 deg. or $090 deg. by a -90 deg. phase shifter 4, and the output signal of the phase shifter 4 is divided by the input color burst signal in a divider 5, and the output signal of the divider 5 is subjected to inverse trigonometric function arithmetic by a tan inverse trigonometric function arithmetic unit 6, and the output signal of the unit 6 is delayed in ahone clock delay circuit 7 by one sampling period, and the difference between te output signal of the unit 6 and that of the delay circuit 7 is operated by an adder 8 to obtain the AFC signal. The output signal of the unit 6 is subjected to trigonometric function arithmetic in an sin trigonometric function arithmetic unit 10, and the output signal of the unit 10 is divided by the input color burst signal or the output signal of the phase shifter 4 in a divider 11 to obtain the ACC signal. The difference of phase between the output signal of the unit 6 and a reference signal is operated by an adder 18 to obtain the APC signal.

Cosine transformation device

Abstract: PURPOSE:To attain high-speed cosine transformation by using a real number multiplier applying N/2 time real number multiplication and a butterfly adder in common with inverse cosine transformation device to use it easily as an inverse cosine transformation device through switching and applying the number of times of real number multiplication of N/2log2N. CONSTITUTION:After an input value is converted by butterfly adder 24, a part is multiplied to a real number by a multiplier 27. The result is transformed by a butterfly adder 25, a part is multiplied to the real number by a real number multiplied 28 and added by an adder 30. Moreover, data is processed similarly by a buffer fly adder 26, a real number multiplied 29 and an adder 31 similarly, multiplied by a multiplier 32 and then outputted. Since the division of 2's power is processed by a multiplier 32, 1/4 and 1/2 time are realized by one-and two-bit shift processing. In this case, the butterfly adders 24, 25, 26 and the real number multipliers 27, 28, 29, 32 are of the same constitution as those of a conventional inverse cosine transformation device. Thus, in using this transformation device, many circuit are used in common for the inverse cosine transformation device.

3000 solved problems in calculus

Abstract: Inequalities absolute value lines circles functions and their graphs limits continuity the derivative the chain rule trigonometric functions and their derivatives Rolle's theorem, the mean value theorem and the sign of the derivative higher-order derivatives and implicit differentiation maxima and minima related rates curve sketching (graphs) applied maximum and minimum problems rectilinear motion approximation by differentials antiderivatives (indefinite integrals) the definite integral and the fundamental theorem of calculus area and arc length volume the natural logarithm exponential functions l"Hopital's rule exponential growth and decay inverse trigonometric functions integration by parts trigonometric integrands and substitutions integration by rational functions - the method of partial functions integrals for surface area, work, centroids improper integrals planar vectors parametric equations vector functions, curvilinear motion polar coordinates infinite sequences infinite series power series Taylor and MacLaurin series vectors in space, lines and planes functions of several variables partial derivatives directional derivatives and the gradient extreme values multiple integrals and their applications vector functions in space divergence and curl, line integrals differential equations.

Schaum's 3000 solved problems in calculus

Abstract: Inequalities absolute value lines circles functions and their graphs limits continuity the derivative the chain rule trigonometric functions and their derivatives Rolle's theorem, the mean value theorem and the sign of the derivative higher-order derivatives and implicit differentiation maxima and minima related rates curve sketching (graphs) applied maximum and minimum problems rectilinear motion approximation by differentials antiderivatives (indefinite integrals) the definite integral and the fundamental theorem of calculus area and arc length volume the natural logarithm exponential functions l"Hopital's rule exponential growth and decay inverse trigonometric functions integration by parts trigonometric integrands and substitutions integration by rational functions - the method of partial functions integrals for surface area, work, centroids improper integrals planar vectors parametric equations vector functions, curvilinear motion polar coordinates infinite sequences infinite series power series Taylor and MacLaurin series vectors in space, lines and planes functions of several variables partial derivatives directional derivatives and the gradient extreme values multiple integrals and their applications vector functions in space divergence and curl, line integrals differential equations.