Showing papers on "Inverse trigonometric functions published in 1991"

Signal detection system and burst demodulator

Abstract: PURPOSE: To omit excessive detection time and to perform burst demodulation at high speed with preamble shorter than ever by performing signal detection simultaneously with bit synchronization based on the observation of bit correla tion amplitude. CONSTITUTION: The phase correlation of an input envelope with a complex sine wave that oscillates by the almost same frequency as a bit frequency is taken by a phase correlation detecting means 5, and after the averaging operation is applied to it, bit correlation amplitude is calculated by an absolute value calculation means 7. The leading edge of the amplitude is observed, and a signal can be detected. Simultaneously, the inverse tangent of phase correlation output is found by an inverse tangent calculation means 11, and a bit timing can be obtained. A signal point is sampled by an obtained timing based on a signal detection timing. The inverse modulation of input is performed by known preamble, and generation and phase demodulation can be performed by using the nonmodulated signal. COPYRIGHT: (C)1994,JPO&Japio

Electronic measuring apparatus and estimation of frequency

Abstract: PURPOSE: To estimate an accurate frequency in a short time by measuring a phase and calculating the shifting speed of the phase. CONSTITUTION: This instrument consists of analog signal input 12, a frequency conversion stage 14, and a processing circuit 16. An A/D converter 24 of the processing circuit 16 samples an IF signal periodically and outputs a series of corresponding digital samples. A real signal sample and a false signal sample are applied to a 1st arithmetic processor 34, which calculate a real and a false quotient corresponding to each pair of samples and determines the tangent of an IF signal phase angle. Further, the processor 34 determines the phase of the IF signal by executing an inverse tangent function. A 2nd processor 38 takes a linear recursive analysis to determine the best estimated value of the phase shifting speed. A 3rd processor 40 is provided with frequency information on a local oscillator 20 which is mixed with the input signal, so the frequency of the initial input signal can be calculated.

Fast approximation to the arctangent

Abstract: Publisher Summary This chapter describes the fast approximation to the arctangent. Given the components of a vector { dx , dy ), the inverse trigonometric arctangent function is used to determine precisely the angle that the vector makes with respect to the x axis. The function arctan2( dy , dx ) is provided in many program libraries so that the function can be defined for all values of dx and dy (except the single case where both dx and dy are zero). A useful measure of vector angle can be constructed by a piecewise continuous function, using only three comparisons, one division, and one or two add/subtract operations. This represents significantly fewer operations than a standard implementation of arctan2. The segments of the piecewise continuous function are determined by the octant in which the vector lies. The octant can be determined by three comparisons of dx with respect to 0, dy with respect to 0, and dx with respect to dy .

Device and method for evaluating inverse trigonometric functions

Abstract: A method and device are provided for processing an input value to provide an output inverse trigonometric function value of the input value. It substantially comprises a method and device comprising a modifier (104) for modifying the input value to obtain an approximation value, a correction factor generator (108) for determining at least one correction factor, a first function generator (106) for generating at least one intermediate function value, being substantially an inverse trigonometric function value of the approximation value, and a combiner (110) for combining the intermediate function value with at least one correction factor to determine an output inverse trigonometric function value.