- Faridabad, Haryana, India
Abstract Numerical dierentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simplied to one of the nite dierence approximations based on Taylor series. In this paper, we have presented closed-form... more
Abstract Numerical dierentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simplied to one of the nite dierence approximations based on Taylor series. In this paper, we have presented closed-form expressions of these approximations of arbitrary order for rst and higher derivatives. A comparison of the three types of approximations is given with an ideal digital dierentiator
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Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were... more
Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.
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Research Interests: Applied Mathematics, Finite element method, Derivation, Applied Mathematics and Computational Science, Computer Program, and 7 moreTaylor Series, Digital Filter Design, Finite Difference, Numerical Analysis and Computational Mathematics, Frequency Response, Electrical And Electronic Engineering, and Numerical Differentiation
Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were... more
Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.
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A new type of Taylor series based finite difference approximations of higher-degree derivatives of a function are presented in closed forms, with their coefficients given by explicit formulas for arbitrary orders. Characteristics and... more
A new type of Taylor series based finite difference approximations of higher-degree derivatives of a function are presented in closed forms, with their coefficients given by explicit formulas for arbitrary orders. Characteristics and accuracies of presented approximations and already presented central difference higher-degree approximations are investigated by performing example numerical differentiations. It is shown that the presented approximations are more
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New designs of highly efficient low/high- and mid-pass/stop (centre-symmetric band-pass/stop) FIR non-recursive digital filters are presented. The designs are based on the modulation property of DFT, applied to the already presented... more
New designs of highly efficient low/high- and mid-pass/stop (centre-symmetric band-pass/stop) FIR non-recursive digital filters are presented. The designs are based on the modulation property of DFT, applied to the already presented MAXFLAT halfband low-pass filters. The presented filters have explicit formulas for their tap-coefficients, and therefore are very easy to design. They have highly smooth frequency response and wider transition regions like MAXFLAT filters. The design formulae are modified to give new classes of low/high- and mid-pass/stop filters, for which, like in equiripple filters, the transition bandwidth can be reduced by increasing the size of ripple on magnitude response. It is shown, with the help of design examples, that the performance of these filters is comparable to that of equiripple filters. Copyright © 2001 John Wiley & Sons, Ltd.
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Maximal linear FIR digital differentiators are preferred over others, like minimax designs, for narrow band applications. Most of the existing maximally linear designs achieve maximal linearity at zero frequency, and relatively lower... more
Maximal linear FIR digital differentiators are preferred over others, like minimax designs, for narrow band applications. Most of the existing maximally linear designs achieve maximal linearity at zero frequency, and relatively lower attention has been given to the designs accurate in mid and higher frequency bands. We present a simple design accurate for midband frequencies, by forcing the maximal linearity constraints at half of the Nyquist frequency. The design problem is formulated as the solution of a system of linear equations, obtained by imposing maximal linearity constraints to the general frequency response of the filter. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored and used in derivation of the explicit formulas for the impulse response coefficients.
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Research Interests: Motion control, Control Systems, Differential Equations, Nonlinear filters, Impulse response, and 10 moreFrequency, Low Power Fir Digital Filter, FIR filters, Digital Filters, Linear Phase, Linearity, Linear Equations, Electrical And Electronic Engineering, Finite Impulse Response (FIR), and Finite Impulse Response Filter
In this paper, we present a new method for 3D model recognition. Unlike other approaches, our model recognition is accomplished based on a plane which describes a 3D model and an eigen-model algorithm. By mapping a 3D model into a virtual... more
In this paper, we present a new method for 3D model recognition. Unlike other approaches, our model recognition is accomplished based on a plane which describes a 3D model and an eigen-model algorithm. By mapping a 3D model into a virtual cylinder around the model, we get the 3D model aspect information on an unfolded cylinder as a 2D image,