Abstract
This chapter provides the basic mathematical fundamentals that are used throughout the book. These concepts allow a more precise understanding of the impact of process variations on the performance modern digital integrated circuits. First, the chapter gives an introduction to the probability and statistical theory. Then, discrete and continuous random variables are described. Next, the chapter describes the mean and variance, which enable the characterization of random variable functions. Some major distributions of random variables such as the uniform and normal distributions are described. Covariance and correlation that are two important concepts in the context of this book are explained. Statistical SUM operator for independent and correlated random variables is described. Besides, a brief explanation of the theorem of Taylor is given.
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Champac, V., Garcia Gervacio, J. (2018). Mathematical Fundamentals. In: Timing Performance of Nanometer Digital Circuits Under Process Variations. Frontiers in Electronic Testing, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-75465-9_2
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DOI: https://doi.org/10.1007/978-3-319-75465-9_2
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