By Henry Hamburger
this article makes in-depth explorations of a huge variety of theoretical issues in computing device technology. It plunges into the functions of the summary thoughts with a purpose to confront and handle the skepticism of readers, and instill in them an appreciation for the usefulness of conception. A two-part presentation integrates good judgment and formal language—both with purposes. bankruptcy themes conceal mathematical preliminaries, propositional good judgment, proving issues: why and the way, predicate common sense, proving with predicates, software verification, common sense programming, language versions for laptop technology, language types, finite automata and their languages, common expressions, Lex: a device for construction lexical scanners, context-free grammars, pushdown automata and parsing, and turing machines. For destiny laptop scientists.
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Extra info for Logic and Language Models for Computer Science
Second, it is often desirable to recalculate the mean and standard deviation as new samples are acquired and added to the signal. We will call this type of calculation: running statistics. While the method of Eqs. 2-1 and 2-2 can be used for running statistics, it requires that all of the samples be involved in each new calculation. This is a very inefficient use of computational power and memory. A solution to these problems can be found by manipulating Eqs. 2-1 and 2-2 to provide another equation for calculating the standard deviation: EQUATION 2-3 Calculation of the standard deviation using running statistics.
Take each number generated by this equation, multiply it by the desired standard deviation, and add the desired mean. Chapter 2- Statistics, Probability and Noise 31 12 11 pdf a. 5, Ú = 1/û12 10 9 8 7 6 5 4 3 2 1 0 0 16 32 48 64 80 Sample number 96 112 128 127 12 11 pdf b. 0, Ú = 1/û6 10 9 8 7 6 5 4 3 2 1 0 0 16 32 48 64 80 Sample number 96 112 128 127 12 11 pdf c. X = RND+RND+ ... 0, Ú = 1 10 9 8 7 6 5 4 3 2 1 0 0 16 32 48 64 80 Sample number 96 112 128 127 FIGURE 2-10 Converting a uniform distribution to a Gaussian distribution.
In (d), the frequency of the analog sine wave is greater than the Nyquist frequency (one-half of the sampling rate). This results in aliasing, where the frequency of the sampled data is different from the frequency of the continuous signal. Since aliasing has corrupted the information, the original signal cannot be reconstructed from the samples. Two terms are widely used when discussing the sampling theorem: the Nyquist frequency and the Nyquist rate. Unfortunately, their meaning is not standardized.