# Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

@inproceedings{Shynk2012ProbabilityRV, title={Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications}, author={John J. Shynk}, year={2012} }

Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong…

## 86 Citations

### Processing and Frequency Analysis of Random Signals

- Computer ScienceRandom Processes with Applications to Circuits and Communications
- 2019

This chapter discusses the effect of basic signal processing operations performed on random signals, such as linear filtering and modulation, and presents Rice’s model of bandpass WSS signals, which is used routinely to analyze modulated bandpass communications or radar receivers by examining an equivalent baseband problem.

### Optimum Parameter Estimation Under Additive Cauchy-Gaussian Mixture Noise

- Mathematics, Engineering
- 2020

An M-estimator with pseudo-Voigt function is developed to improve the computational complexity of MLE and results indicate the superior of both proposals, which can attain the Cramer-Rao lower bound.

### Stochastic integration Student's-t filter

- Mathematics2017 20th International Conference on Information Fusion (Fusion)
- 2017

The paper deals with the nonlinear state estimation of stochastic dynamic systems with a special focus on coping with outliers appearing in the system using the generic Student's-t filter.

### Characteristic function based performance index for Bayesian filters

- Computer Science2016 19th International Conference on Information Fusion (FUSION)
- 2016

The paper deals with state estimation of nonlinear stochastic dynamic systems in the Bayesian framework with an introduction of a performance index, which can inform about working conditions of the filter and about the quality of approximations used by the filter.

### Simulation of two-dimensional distribution laws of random correlated quantities of natural-climatic factors in context of probabilistic assessment of reliability of hydraulic structures of cascades of hydroschemes

- EngineeringE3S Web of Conferences
- 2021

When performing calculations to assess reliability of hydraulic structures of cascades of hydroschemes on the basis of probabilistic methods, the necessity to simulate random natural-climatic…

### Entropy Power, Autoregressive Models, and Mutual Information

- Computer ScienceEntropy
- 2018

The quantity defined by Shannon in 1948, the entropy rate power, is considered, and it is shown that the log ratio of entropy powers equals the difference in the differential entropy of the two processes.

### Improved Non-coherent Communication Systems Using Noise Reduction Chaotic ON–OFF Keying (NR-COOK) Techniques

- Computer ScienceWirel. Pers. Commun.
- 2020

Closed form expression for bit error rate (BER) of the proposed NR-COOK system is derived and analyzed under multipath fading channel and are validated through simulation results to demonstrate performance improvement over conventional non coherent schemes.

### Estimation under additive Cauchy-Gaussian noise using Markov chain Monte Carlo

- Computer Science2014 IEEE Workshop on Statistical Signal Processing (SSP)
- 2014

This paper considers an impulsive mixture noise process, which commonly comes across in applications such as multiuser radar communications, astrophysical imaging in the microwave range and kick detection in oil drilling, and proposes using a Markov chain Monte Carlo method, in particular the Metropolis-Hastings algorithm.