The small probability of collision of the Earth and a comet can become very great in adding over a long sequence of centuries. It is easy to picture the effects of this impact on the Earth. The axis and the motion of rotation have changed, the seas abandoning their old position. Pierre-Simon Laplace PROBABILITY MODELS Random Signals and Stochastic Processes Probabilistic Models Stationary and Non-stationary Processes Expected Values of a Process Some Useful Classes of Random Processes Transformation of a Random Process Summary P robability models form the foundation of information theory. Information itself is quantified in terms of the logarithm of probability. Probability models. | Advanced Digital Signal Processing and Noise Reduction Second Edition. Saeed V. Vaseghi Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-62692-9 Hardback 0-470-84162-1 Electronic 3 The small probability of collision of the Earth and a comet can become very great in adding over a long sequence of centuries. It is easy to picture the effects of this impact on the Earth. The axis and the motion of rotation have changed the seas abandoning their old position. Pierre-Simon Laplace PROBABILITY MODELS Random Signals and Stochastic Processes Probabilistic Models Stationary and Non-stationary Processes Expected Values of a Process Some Useful Classes of Random Processes Transformation of a Random Process Summary Probability models form the foundation of information theory. Information itself is quantified in terms of the logarithm of probability. Probability models are used to characterise and predict the occurrence of random events in such diverse areas of applications as predicting the number of telephone calls on a trunk line in a specified period of the day road traffic modelling weather forecasting financial data modelling predicting the effect of drugs given data from medical trials etc. In signal processing probability models are used to describe the variations of random signals in applications such as pattern recognition signal coding and signal estimation. This chapter begins with a study of the basic concepts of random signals and stochastic processes and the models that are used for the characterisation of random processes. Stochastic processes are classes of signals whose fluctuations in time are partially or completely random such as speech music image time-varying channels noise and video. Stochastic signals are completely described in terms of a probability model but can also be characterised with relatively simple statistics such as the mean the correlation and the power spectrum. We study the concept of ergodic stationary processes
