The linear interpolation method: a sampling theorem approach

A lecture note introducing the sampling theorem as an interpolation method is presented. The relationship between piecewise linear approximation and the sampling theorem is highlighted by the use of triangular pulses instead of sampling functions. Furthermore, a comparison of the linear interpolation with a series on a nonorthogonal basis composed of equally spaced triangular pulses is provided. The interpolation uses the sample values of the function whereas the series coefficients are obtained by minimizing the quadratic error between the original function and the series.

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MULTISCALE TREND ANALYSIS

Fractals ◽

10.1142/s0218348x04002604 ◽

2004 ◽

Vol 12 (03) ◽

pp. 275-292 ◽

Cited By ~ 12

Author(s):

ILYA ZALIAPIN ◽

ANDREI GABRIELOV ◽

VLADIMIR KEILIS-BOROK

Keyword(s):

Time Series ◽

Trend Analysis ◽

Linear Approximation ◽

Piecewise Linear ◽

Linear Interpolation ◽

Piecewise Linear Approximation ◽

Linear Approximations ◽

Piecewise Linear Approximations ◽

Original Time ◽

Internal Level

This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated, and on its base, a computationally effective algorithm is constructed for decomposition of a time series into a hierarchy of trends (local linear approximations) at different scales. The top of the hierarchy is the global linear approximation over the whole observational interval, the bottom is the original time series. Each internal level of the hierarchy corresponds to a piecewise linear approximation of analyzed series. Possible applications of the introduced Multiscale Trend Analysis (MTA) go far beyond the linear interpolation problem: This paper develops and illustrates methods of self-affine, hierarchical, and correlation analyses of time series.

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Proposal of tool path generation for recycle pad in Chemical Mechanical Polishing based on piecewise linear interpolation method

2014 IEEE/SICE International Symposium on System Integration ◽

10.1109/sii.2014.7028079 ◽

2014 ◽

Author(s):

Tomoyuki Kawaguchi ◽

Yuto Takagi ◽

Ryota Sakamoto ◽

Ken'ich Yano ◽

Tatsutoshi Suzuki

Keyword(s):

Chemical Mechanical Polishing ◽

Tool Path ◽

Interpolation Method ◽

Piecewise Linear ◽

Linear Interpolation ◽

Tool Path Generation ◽

Mechanical Polishing ◽

Path Generation ◽

Piecewise Linear Interpolation ◽

Linear Interpolation Method

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Trajectory Optimization using Piecewise Linear Approximation Dynamic Programming

AEROSPACE TECHNOLOGY JAPAN THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES ◽

10.2322/astj.14.33 ◽

2015 ◽

Vol 14 (0) ◽

pp. 33-41

Author(s):

Haruki MATSUDA ◽

Akinori HARADA ◽

Yoshikazu MIYAZAWA

Keyword(s):

Dynamic Programming ◽

Linear Approximation ◽

Trajectory Optimization ◽

Piecewise Linear ◽

Piecewise Linear Approximation

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A Three-Dimensional Finite Difference Time Domain - Perfectly Matched Layer Algorithm Based on Piecewise-Linear Approximation for Linear Dispersive Media

10.21236/ada379806 ◽

2000 ◽

Author(s):

S. J. Yakura ◽

David Dietz

Keyword(s):

Finite Difference ◽

Linear Approximation ◽

Time Domain ◽

Finite Difference Time Domain ◽

Piecewise Linear ◽

Three Dimensional ◽

Perfectly Matched Layer ◽

Piecewise Linear Approximation ◽

Dispersive Media ◽

Difference Time

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Applying Piecewise Linear Approximation for DNN Non-Linear Activation Functions to Bfloat16 MACs

2021 International Conference on Electronics, Information, and Communication (ICEIC) ◽

10.1109/iceic51217.2021.9369759 ◽

2021 ◽

Author(s):

Seok Young Kim ◽

Chang Hyun Kim ◽

Seon Wook Kim

Keyword(s):

Linear Approximation ◽

Piecewise Linear ◽

Piecewise Linear Approximation ◽

Activation Functions ◽

Non Linear

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An experimental study on optimal spark timing control for improved performance of a flex fuel vehicle engine

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1177/0954407019869773 ◽

2019 ◽

Vol 234 (5) ◽

pp. 1294-1303

Author(s):

Junsang Yoo ◽

Taeyong Lee ◽

Pyungsik Go ◽

Yongseok Cho ◽

Kwangsoon Choi ◽

...

Keyword(s):

Empirical Equation ◽

Interpolation Method ◽

Linear Interpolation ◽

Combustion Characteristics ◽

Combustion Stability ◽

Timing Control ◽

Vehicle Engine ◽

Spark Timing ◽

Linear Interpolation Method ◽

Blended Fuels

In the American continent, the most frequently used alternative fuel is ethanol. Especially in Brazil, various blends of gasoline–ethanol fuels are widely spread. The vehicle using blended fuel is called flexible fuel vehicle. Because of several selections for the blending ratios in gas stations, the fuel properties may vary after refueling depending on a driver’s selection. Also, the combustion characteristics of the flexible fuel vehicle engine may change. In order to respond to the flexible fuel vehicle market in Brazil, a study on blended fuels is performed. The main purpose of this study is to enhance performance of the flexible fuel vehicle engine to target Brazilian market. Therefore, we investigated combustion characteristics and optimal spark timings of the blended fuels with various blending ratios to improve the performance of the flexible fuel vehicle engine. As a tool for prediction of the optimal spark timing for the 1.6L flexible fuel vehicle engine, the empirical equation was suggested. The validity of the equation was investigated by comparing the predicted optimal spark timings with the stock spark timings through engine tests. When the stock spark timings of E0 and E100 were optimal, the empirical equation predicted the actual optimal spark timings for blended fuels with a good accuracy. In all conditions, by optimizing spark timing control, performance was improved. Especially, torque improvements of E30 and E50 fuels were 5.4% and 1.8%, respectively, without affecting combustion stability. From these results, it was concluded that the linear interpolation method is not suitable for flexible fuel vehicle engine control. Instead of linear interpolation method, optimal spark timing which reflects specific octane numbers of gasoline–ethanol blended fuels should be applied to maximize performance of the flexible fuel vehicle engine. The results of this study are expected to save the effort required for engine calibration when developing new flexible fuel vehicle engines and to be used as a basic strategy to improve the performance of other flexible fuel vehicle engines.

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