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.

Stereoscopic method and a device for implementation thereof

Abstract: The invention relates to stereoscopic video equipment and can be used to design stereoscopic TV sets and monitors with a possibility to observe stereo images both glasses-free and with use of passive glasses while keeping a possibility to observe monoscopic images. These possibilities are provided in the method and in the device by means of a light flux elliptical polarization modulator with polarization modulation parameters determined by inverse trigonometric functions such as arctg, arcctg, arccos and arcsin (or their combinations) from algebraic relations between squared amplitudes of image temporal scanning signals, that permits with help of spatially-periodic polarization selector to obtain the images of the left and the right views in the left and right observation areas.

Hardware Implementations of Fixed-Point Atan2

Abstract: The atan2 function computes the polar angle arctan(y/x) of a point given by its cartesian coordinates. It is widely used in digital signal processing to recover the phase of a signal. This article studies for this context the implementation of atan2 with fixed-point inputs and outputs. It compares the prevalent CORDIC shift-and-add algorithm to two multiplier-based techniques. The first one computes the bivariate atan2 function as the composition of two univariate functions: the reciprocal, and the arctangent, each evaluated using bipartite or polynomial approximation methods. The second technique directly uses piecewise bivariate polynomial approximations of degree 1 or 2. Each of these approaches requires a relevant argument reduction, which is also discussed. All the algorithms are last-bit accurate, and implemented with similar care in the open-source FloPoCo framework. Based on synthesis results on FPGAs, their relevance domains are discussed.

Highly accurate zero crossings for frequency determination

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.