scholarly journals Symmetric quadratic tetration interpolation using forward and backward operation combination

2022 ◽  
Vol 12 (2) ◽  
pp. 1893
Author(s):  
Chapkit Charnsamorn ◽  
Suphongsa Khetkeeree
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Signal To Noise Ratio ◽  
Signal Reconstruction ◽  
Sine Wave ◽  
Cubic Spline ◽  
Individual Characteristics ◽  
Second Order ◽  
Cubic Spline Interpolation ◽  
Reconstruction Performance

The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.

scholarly journals Error Analysis for a Noisy Lacunary Cubic Spline Interpolation and a Simple Noisy Cubic Spline Quasi Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Feng-Gong Lang ◽  
Xiao-Ping Xu
Keyword(s):  
Error Analysis ◽  
Error Bounds ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
The Other ◽  
Cubic Spline Interpolation ◽  
Numerical Tests ◽  
New Methods ◽  
Noisy Function

We mainly present the error analysis for two new cubic spline based methods; one is a lacunary interpolation method and the other is a very simple quasi interpolation method. The new methods are able to reconstruct a function and its first two derivatives from noisy function data. The explicit error bounds for the methods are given and proved. Numerical tests and comparisons are performed. Numerical results verify the efficiency of our methods.

Gait Planning of Humanoid Robot Based on ZMP and Cubic Spline Interpolation

2013 ◽  
Vol 427-429 ◽  
pp. 1394-1397 ◽  
Author(s):  
Xian Lun Wang ◽  
Ping Li ◽  
Fei Qi Yang
Keyword(s):  
Humanoid Robot ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Smooth Transition ◽  
Cubic Spline Interpolation ◽  
Gait Planning ◽  
Inverted Pendulum Model ◽  
Point Equation ◽  
The Impact

Teaching programming and manual programming are usually used to realize gait planning of humanoid robot. Many methods are lack of the adjustment of center of gravity and lead to the robot walking instability. The gait planning of humanoid robot is solved based on the Linear Inverted Pendulum Model and Zero Moment Point equation in this paper. Two feet trajectories are also planned to realize the smooth transition and overcome the impact during walking with the cubic spline interpolation method. The validation and feasibility of the method proposed in the paper are proved by the results of simulation and experiments.

scholarly journals Vector Autoregressive X (VARX) Modeling for Indonesian Macroeconomic Indicators and Handling Different Time Variations with Cubic Spline Interpolation

2019 ◽  
pp. 175-180
Author(s):  
Ayu Septiani ◽  
I Made Sumertajaya ◽  
Muhammad Nur Aidi
Keyword(s):  
Economic Growth ◽  
Interest Rates ◽  
Time Series Data ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Series Data ◽  
Cubic Spline Interpolation ◽  
Vector Autoregressive ◽  
Time Variations

This study discusses data handling that has different time variations (for example, data available in quarterly form but the desired data is monthly) in this case the GDP variable in the quarter series, while the other five variables use monthly series, whereas in multivariate analysis the data condition must be the same, then an approach is taken to reduce monthly data from quarterly data using the interpolation method. Therefore, before conducting the VARX analysis the author interpolated GDP data from the quarter to monthly by interpolation. After the data is ready, VARX modeling of the exchange rate, economic growth (GDP), interest rates on Bank Indonesia Certificates (SBI), and inflation as endogenous variables and US interest rates (FFR) and US inflation as exogenous variables. The purpose of this study is to implement and evaluate the performance of Cubic Spline interpolation methods for time series data that have different time variations. Build VARX models and predict exchange rates, economic growth (GDP), SBI interest rates, and inflation based on US interest rates (FFR) and US inflation with the best models. Meanwhile, the interpolation method used by researchers to estimate the monthly value of the GDP variable based cubic spline interpolation. Based on the AIC value of the smallest VARX model obtained at 240.6668 so the best model obtained is the VARX (4.0) model.

Interpolation Method Research and Precision Analysis of GPS Satellite Position

2018 ◽  
Vol 6 (3) ◽  
pp. 277-288
Author(s):  
Jianmin Wang ◽  
Yabo Li ◽  
Huizhong Zhu ◽  
Tianming Ma
Keyword(s):  
Lagrange Interpolation ◽  
Hermite Interpolation ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Newton Interpolation ◽  
Cubic Spline Interpolation ◽  
Satellite Position ◽  
Precise Ephemeris ◽  
Better Than

Abstract According to the precise ephemeris has only provided satellite position that is discrete not any time, so propose that make use of interpolation method to calculate satellite position at any time. The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation, Newton interpolation, Hermite interpolation, Cubic spline interpolation method, Chebyshev fitting method respectively, which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst, the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore, Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.

Cubic Spline Interpolation Method for the Envelope Tracking of Middle and Low Frequency Voltage Flicker

2014 ◽  
Vol 960-961 ◽  
pp. 704-709 ◽  
Author(s):  
Xiu Fang Jia ◽  
Hai Qing An ◽  
Shao Guang Zhang
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Low Frequency ◽  
Cubic Spline ◽  
Time Varying ◽  
Envelope Tracking ◽  
Low Frequencies ◽  
Cubic Spline Interpolation ◽  
Signal Simulation ◽  
Voltage Flicker

Flicker envelope tracking is the key of analyzing voltage flicker signal. A novel method, i.e., cubic spline interpolation method is applied in the detection of the voltage flicker envelope. The typical flicker signals, such as one or multi-frequencies and frequency time-varying flicker signal are selected and analyzed by this method. Simulation results indicate that this method is effective in the detection of the envelope of voltage flicker signal. Results of one or multi-frequencies flicker signal simulation show that, when flicker frequency is less than 15Hz , the error of this method is quite tiny. The detection precision of this method is higher, especially in the scope of low frequencies of flicker and this method makes up for the disadvantage of square demodulation. Furthermore, results of frequency time-varying flicker signal simulation show that, the occurrence and recover time of voltage flicker signal can be accurately detected by cubic spline interpolation method.

Interpolation Technology and its Application in Damage Analysis of Bridge Structure

2012 ◽  
Vol 446-449 ◽  
pp. 1261-1265
Author(s):  
Ke Ding
Keyword(s):  
Test Data ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Modal Parameters ◽  
Damage Analysis ◽  
Bridge Structure ◽  
Cubic Spline Interpolation ◽  
Structure Damage ◽  
Damage Location

The damage analysis based on the modal parameters usually need to compare the test data with the computed data by theoretical analysis. In bridge structure damage analysis, it is impossible that the sensors are set at every node. So the test data need to be extended to every node by using interpolation technology. In the paper, three interpolation methods, cubic interpolation method, cubic spline interpolation method and sinc interpolation method, are introduced. Their applications in bridge structure damage analysis are discussed. The experiment results show that the best interpolation method is cubic spline interpolation method. Using the data processed by interpolation technology can well obtain the damage location of bridge.

scholarly journals Selection Method of Modulation Index and Frequency ratio for Getting the SPWM Minimum Harmonic of Single Phase Inverter

2021 ◽  
Vol 9 (1) ◽  
pp. 75-91
Author(s):  
Ant. Ardath Kristi ◽  
Bambang Susanto ◽  
Agus Risdiyanto ◽  
Agus Junaedi ◽  
Anwar Muqorobin ◽  
...  
Keyword(s):  
Frequency Ratio ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Modulation Index ◽  
Generation Process ◽  
Cubic Spline Interpolation ◽  
Harmonic Content ◽  
Single Phase Inverter ◽  
Lc Filter

Harmonic content is an important parameter in relation to the power generated by inverter. In power conversion technology of inverter, sinusoidal pulse width modulation (SPWM) is the most popular used by many researchers. The advantages of SPWM inverter operation as a conversion technique compared to other inverter types can be seen from the low harmonic distortion in the output voltage of inverter. Therefore, the SPWM signal generation process becomes a determining factor for the performance of the overall system. This paper present the method for selecting the modulation index (ma) and frequency ratio (mf) using Cubic Spline Interpolation to get minimum harmonic of SPWM inverter that generated. Both parameters controlled with varied values digitally using microcontroller to generate SPWM, then the output of inverter with and without LC filter was investigated. The results show that the use of Cubic Spline Interpolation method in the selection of ma and mf precisely managed to produce SPWM inverter with minimum harmonic content. At the inverter output, the use of LC filter is not only useful for converting SPWM signals to sinusoidal waveforms but can also reduce harmonic content significantly less than 3 %.

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