Comparative evaluation of interpolation methods for the directivity of musical instruments

Measurements of the directivity of acoustic sound sources must be interpolated in almost all cases, either for spatial upsampling to higher resolution representations of the data, for spatial resampling to another sampling grid, or for use in simulations of sound propagation. The performance of different interpolation techniques applied to sparsely sampled directivity measurements depends on the sampling grid used but also on the radiation pattern of the sources themselves. Therefore, we evaluated three established approaches for interpolation from a low-resolution sampling grid using high-resolution measurements of a representative sample of musical instruments as a reference. The smallest global error on average occurs for thin plate pseudo-spline interpolation. For interpolation based on spherical harmonics (SH) decomposition, the SH order and the spatial sampling scheme applied have a strong and difficult to predict influence on the quality of the interpolation. The piece-wise linear, spherical triangular interpolation provides almost as good results as the first-order spline approach, albeit with on average 20 times higher computational effort. Therefore, for spatial interpolation of sparsely sampled directivity measurements of musical instruments, the thin plate pseudo-spline method applied to absolute-valued data is recommended and, if necessary, a subsequent modeling of the phase.

Further Analysis of the Passive Dynamics of the Compass Biped Walker and Control of Chaos via Two Trajectory Tracking Approaches

This work consists in analyzing and controlling the walk of the compass-type bipedal walker in order to stabilize its passive dynamic gait. The dynamic walking of the compass-gait walker is modeled by an impulsive hybrid nonlinear system. This impulsive hybrid nature is considered very complex as it can generate unwanted phenomena such as chaos and bifurcations. We show first by means of bifurcation diagrams and by varying the slope angle of the walking surface and also the length of the lower leg segment that the passive dynamic walking exhibits successive period-doubling bifurcations leading to chaos. Furthermore, in order to control chaos and hence obtain one-periodic walking behavior, we propose two control approaches based on tracking a desired trajectory. The first method consists in tracking the one-periodic passive dynamic walking generated by the compass model itself. The second control method lies in following a planned trajectory using the 4th-order Spline function. An optimization method is also achieved to design the parameters of the desired trajectory. Some features of the period-1 passive gait are used in the design of such Spline trajectory. Finally, we show some simulation results revealing the efficiency of the two proposed control methods in the control of the chaotic passive gait of the compass-gait walker. Moreover, we demonstrate the stabilization of the bipedal locomotion of the compass biped walker on different slopes: descending and ascending inclined planes and walking on a level ground. A comparison with the OGY-based control method is also performed to further show the superiority of these two control approaches.

Development of 3D Models of Knits from Multi-Filament Ultra-Ftrong Yarns for Theoretical Modelling of Air Permeability

The work is devoted to the study of the geometric parameters of a knitted loop. It has been found that the optimal model is a loop model detailed at the yarn level, which considers the change in the cross-sectional shape and sets the properties of the porous material in accordance with the internal porosity of the yarn. A mathematical description of the coordinates of the characteristic points of the loop and an algorithm for calculating the coordinates of the control vertices of the second order spline, which determine the configuration of the yarn axes in the loop, are presented in this work. To create 3D models, Autodesk AutoCAD software and Structura 3D software, developed in the AutoLisp programming language, were used. The simulation of the air flow process was carried out in the Autodesk CFD Simulation environment. For the experimental investigation, plane knits from 44 tex × 3 linear density ultra-high molecular weight polyethylene yarns were produced, and their air permeability was tested according to Standard DSTU ISO 9237:2003. The results obtained during the laboratory experiment and simulation differed by less than 5%.

FAST AND ACCURATE MULTI-FRAME SUPER-RESOLUTION OF SATELLITE IMAGES

Recent constellations of small satellites, such as Planet’s SkySats, offer new acquisition modes where very short videos or bursts of images are acquired instead of a single still image. Compared to sequences of multi-date images, these sequences of consecutive video frames yield a large redundancy of information within the range of seconds. This redundancy enables to increase the spatial resolution using multi-frame super-resolution algorithms. In this paper, we propose a novel super-resolution method based on a high-order spline interpolation model that combines multiple low-resolution frames to produce a high-resolution image. Moreover this method can be implemented efficiently on GPU to process entire images from real satellite acquisitions. Synthetic and real experiments show that the proposed method is able to recover fine details, and measurements of the resulting resolution indicate a gain of 10 cm / pixel with respect to Planet’s SkySat standard imagery products.

Reconstruction of Piecewise Smooth Multivariate Functions from Fourier Data

In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a method for deriving high order approximation to f using a Padé-like method. Namely, we do this by fitting some Fourier coefficients of the approximant to the given Fourier coefficients of f. Given the Fourier series coefficients of a function on a rectangular domain in Rd, assuming the function is piecewise smooth, we approximate the function by piecewise high order spline functions. First, the singularity structure of the function is identified. For example in the 2D case, we find high accuracy approximation to the curves separating between smooth segments of f. Secondly, simultaneously we find the approximations of all the different segments of f. We start by developing and demonstrating a high accuracy algorithm for the 1D case, and we use this algorithm to step up to the multidimensional case.

Numerical Solution for A Class of Fractional Variational Problem via Second Order B-Spline Function

In this paper, we solve a class of fractional variational problems (FVPs) by using operational matrix of fractional integration which derived from second order spline (B-spline) basis function. The fractional derivative is defined in the Caputo and Riemann-Liouville fractional integral operator. The B-spline function with unknown coefficients and B-spline operational matrix of integration are used to replace the fractional derivative which is in the performance index. Next, we applied the method of constrained extremum which involved a set of Lagrange multipliers. As a result, we get a system of algebraic equations which can be solve easily. Hence, the value for unknown coefficients of B-spline function is obtained as well as the solution for the FVPs. Finally, the illustrative examples shown the validity and applicability of this method to solve FVPs.

On approximation of two-dimensional potential and singular operators

The purpose of this paper is the construction of second-order of accuracy quadrature formulas for the numerical calculation of the Vekua types two-dimensional potential and singular integral operators in the unit disk of complex plane. We propose quadrature formulas for these integrals which based on first-order spline approximation of two-dimensional function. MATLAB programs are used for numerical experiments in test examples.

PENERAPAN ANALISIS REGRESI SPLINE UNTUK MENDUGA HARGA CABAI DI JAKARTA

The chili is an important commodity in Indonesia, which has a fairly large price fluctuations. Fluctuations in prices often raises the risk of loss even have contributed to inflation. Chili price data is time series data that is not independent between observations (autocorrelation) and do not spread to normal. In addition, chili price data does not have the diversity of homogeneous data. One method that can be used to predict the pattern of the data is spline regression. The data used in this study is data the average weekly price of chili in Jakarta from January, 2010 to October, 2015. The best spline model is a second order spline models with three knots. The model has a value of Mean Absolute Percentage Error (MAPE) of 9.57% and determination coefficient of 86.41%. The model obtained in this research is already well in predicting the pattern of the chili price, but it was only able to predict well for a period of one month. Prediction chili prices in Jakarta for November are in the range of Rp 35.565. Keywords: chili price, regression, spline.