Triangular function

About: Triangular function is a research topic. Over the lifetime, 184 publications have been published within this topic receiving 2421 citations. The topic is also known as: triangle function & hat function.

Electronic control system

Abstract: A standardized microcontroller-based fuzzy logic processing module (101) for generating control signal values in response to variable input signal values in accordance with constraints imposed by propositions or "rules" stored in memory (117) in a standardized format. Each rule consists of one or more input conditions and an output directive. Each input signal (110) and the output signal (112) values are characterisable by their degree of membership in a predetermined number of fuzzy sets, each fuzzy set being defined by a membership function (119). Each input condition is composed of a reference to a particular input variable, which has been preprocessed into integer (whole number) normalised form and a reference to a membership function. Each output directive includes a reference to a further membership function. Each membership function is implemented by one of a three possible forms of standard membership data structures: a triangular function represented by three data points, a table lookup function represented by a two end data points and the points between these two end points, and an standard shape function composed of a set of data points and a set of reference points used to form a similar shape function by interpolation. Fuzzy logic processing is accomplished by determining the extent to which the input conditions are satisfied by the current values of the input signals in order to develop a rule strength value, and then performing a "centre-of-gravity" determination based on the output membership function values (118) of each satisfied rule integrated over the range of possible output signal values.

A Kinematic Source-Time Function Compatible with Earthquake Dynamics

Abstract: We propose a new source-time function, to be used in kinematic modeling of ground-motion time histories, which is consistent with dynamic propagation of earthquake ruptures and makes feasible the dynamic interpretation of kinematic slip models. This function is derived from a source-time function first proposed by Yoffe (1951), which yields a traction evolution showing a slip-weakening behavior. In order to remove its singularity, we apply a convolution with a triangular function and obtain a regularized source-time function called the regularized Yoffe function. We propose a parameterization of this slip-velocity time function through the final slip, its duration, and the duration of the positive slip acceleration ( Tacc ). Using this analytical function, we examined the relation between kinematic parameters, such as peak slip velocity and slip duration, and dynamic parameters, such as slip-weakening distance and breakdown-stress drop. The obtained scaling relations are consistent with those proposed by Ohnaka and Yamashita (1989) from laboratory experiments. This shows that the proposed source-time function suitably represents dynamic rupture propagation with finite slip-weakening distances.

Fast one-dimensional digital convolution by multidimensional techniques

Abstract: This paper presents two formulations of multi-dimensional digital signals from one-dimensional digital signals so that multidimensional convolution will implement one-dimensional convolution of the original signals. This has reduced an important word length restriction when used with the Fermat number transform. The formulation is very general and includes block processing and sectioning as special cases and, when used with various fast algorithms for short length convolutions, results in improved multiplication efficiency.

Window function influence on phase error in phase-shifting algorithms.

Abstract: We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.

Frequency analysis of digital holography with reconstruction by convolution

Abstract: A coherent optical imaging system consisting of recording a digital hologram by a CCD array and numerical reconstruction of the complex wavefield by the convolution method is subjected to a frequency analysis. The point spread function of such a system is a sinc function whose width depends on the aperture defined by the CCD array and parameters of the transfer function used in the reconstruction. A narrow point spread function and thus a sharp reconstructed image can be obtained by the numerical concept of cascaded free-space propagation, which is introduced and demonstrated.