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- W4255809637 abstract "4.1 Introduction Probability theory is presented here for those who use it in communication theory and signal processing of random waveforms. The concept of sampling a finite power waveform, where a value of time t or n is uniformly chosen over a long time and x(t) or x(n) is observed, is introduced early. All first- and second-order time averages are visualized statistically. The topics covered with some highlights are as follows: Discrete probability theory. The definitions of probability and conditional probability and their evaluation for outcomes of a random phenomenon using relative frequency and axiomatic formulas are given. The theorem of total probability, which elegantly subdivides compound problems into weighted subproblems, is highlighted along with Bayes' theorem. The theory of one random variable. The use of random variables allows for the solution of probabilistic problems using integration and summations for sequences. The bridge from theory to applications is very short as in the relationship between finding the density or mass function of a function of a random variable and the communication problem of finding statistics of a system's random output given statistics of its random input. The theory of two random variables. Joint distribution, density, and mass functions give complete probabilistic information about two random variables and are the key to solving most applications involving continuous and discrete random waveforms and later random processes. Again, the bridge from theory to application is short as in the relationship between finding the density or mass function of a function of two random variables and the communication problem of finding statistics of a system's random output when two random inputs are combined by operations such as summing or multiplying (modulation)." @default.
- W4255809637 created "2022-05-12" @default.
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- W4255809637 date "2002-04-29" @default.
- W4255809637 modified "2023-09-26" @default.
- W4255809637 title "Sampling" @default.
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- W4255809637 doi "https://doi.org/10.1201/9781420041163-4" @default.
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