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## Mathematical background to protection algorithms

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To understand the principles underlying digital protection technology, it is necessary to review briefly the mathematical basis of numerical algorithms. The topics covered in this Chapter therefore include finite differences, numerical differentiation, curve fitting and smoothing, Fourier analysis, Walsh analysis, and the relationship between Fourier and Walsh coefficients. It is not the intention that the material presented should be highly rigorous in the mathematical sense, but rather that it should give a working knowledge of the numerical techniques used and thus provide a basis for the work on specific protection algorithms that is presented in later Chapters.

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