By Robert N. McDonough
The Second Edition is an up to date revision to the authors hugely winning and typical advent to the rules and alertness of the statistical conception of sign detection. This ebook emphasizes these theories which have been came across to be fairly important in perform together with ideas utilized to detection difficulties encountered in electronic communications, radar, and sonar.
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Extra resources for Detection of signals in noise
In that case, rather = X(t;, we think of a than the discrete time random process continuous time process X(t, ,). For each elementary outcome of the experiment, nature selects a time function X(t, which represents a particular waveform that would be observed in the system of interest for each particular choice of point , E '::f in the sample space of the abstract experiment. Such a collection of random variables X(t, ,) indexed by a continuous variable t is called a continuous time random (or stochastic) process.
1) in which t plays the role of a parameter in the integral. Note especially here the notation p [x(t), t] for the density, or just p (x, t) for brevity. The density depends, first, on the values x of the random variable X but also on the time to which those values are indexed. We will often want to deal with values of the random process x(t) at more than one time instant. Then we consider together the two random variables x (t 1), X (t 2) , and their corresponding joint probability density p [Xl (t l ) , X2 (t 2) ; t l , t 2] , or simply p (Xl X2; t l , t 2) .
In this chapter, we extend the ideas of probability to the treatment of waveforms which progress in time in a fashion such that the future is more or less unknowable from observations of the past and present. 1 INTRODUCTION In the last chapter, a random variable X was defined as a real-valued function over the points representing the outcomes of an abstract experiment (J", Pl. At each trial of the experiment, nature chooses exactly one point E g> as elementary outcome, and the experiment in turn presents us with the value of the random variable.
Detection of signals in noise by Robert N. McDonough