3 May 2012 New method for numerical approximations of vector derivatives based on digital signal processing techniques
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Abstract
Accurate propagation models are required for predicting the propagation of electromagnetic waves within complex environments. This paper proposes the use of a new method to accurately compute the divergence and curl of electromagnetic fields. The computation of the derivatives of vector fields is normally approximated using numerical methods such as the Finite-Dierence Time-Domain Method (FDTD), the Finite Integration Technique and the Multi-Resolution Time-Domain Method. These methods are all limited in terms of their accuracy, resolution, computational efficiency and numerical stability. This paper introduces a new method for computing derivatives based on Two-Dimensional (2D) Digital Signal Processing (DSP) techniques. The method involves computing a numerical approximation of the derivative of a function by considering the frequency domain definition of the derivative and designing a 2Dfinite impulse response (FIR) filter that implements the differentiation. Appropriate windowing functions are used to ensure that the FIR response is as close to the ideal 2D differentiator response as possible. This paper provides an example where the curl of a vectorfield is determined using this method and accuracy within a few percent is achieved. The proposed innovative method can be extended to three dimensions and used to find numerical solutions of Maxwells Equations, thus allowing it to be applied to the design of accurate propagation models.
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Henry Brice, Henry Brice, Mohammed Zaki Ahmed, Mohammed Zaki Ahmed, } "New method for numerical approximations of vector derivatives based on digital signal processing techniques", Proc. SPIE 8404, Wireless Sensing, Localization, and Processing VII, 84040D (3 May 2012); doi: 10.1117/12.918918; https://doi.org/10.1117/12.918918
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