Download Signal Detection And Estimation (Artech House Radar Library by Mourad Barkat PDF

By Mourad Barkat

ISBN-10: 1580530702

ISBN-13: 9781580530705

ISBN-10: 1580531016

ISBN-13: 9781580531016

This newly revised variation of a vintage Artech condominium booklet will give you a entire and present realizing of sign detection and estimation. that includes a wealth of recent and improved fabric, the second one variation introduces the options of adaptive CFAR detection and allotted CA-CFAR detection. The publication presents entire causes of the math you want to absolutely grasp the fabric, together with chance conception, distributions, and random techniques.

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Example text

32) i =1 That is, the probability of each value that X can assume must be nonnegative, and the sum of the probabilities over all of the different values must equal 1. 33) The probability density function (PDF) of a discrete random variable that assumes x1, x2, … , is P(x1), P(x2), … , where P(xi) = P(X = xi), i = 1, 2, …. If there is more than one random variable, we denote the PDF of a particular variable X by a subscript X on P as PX (x) . 9 Consider the experiment of rolling two dice. Let X represent the total number that shows up on the upper faces of the two dice.

77). 16 Two-dimensional density function. The joint distribution F XY ( x, y ) has the following properties: 1. 0 ≤ F XY (x, y ) ≤ 1 2. F XY (∞, ∞ ) = 1 3. F XY (−∞,−∞ ) = F XY (x,−∞ ) = F XY (−∞, y ) = 0 4. P(x1 < X ≤ x 2 , Y ≤ y ) = F XY (x 2 , y ) − F XY (x1 , y ) ≥ 0 5. P( X ≤ x , y1 < Y ≤ y 2 ) = F XY (x, y 2 ) − F XY (x, y1 ) ≥ 0 6. 79) by integrating y over all possible values. 82). 86) −∞ fY (y) = ∞ ∫ −∞ Once the marginal distribution functions are known, it becomes simple to determine the conditional distribution functions.

P( X ≤ x , y1 < Y ≤ y 2 ) = F XY (x, y 2 ) − F XY (x, y1 ) ≥ 0 6. 79) by integrating y over all possible values. 82). 86) −∞ fY (y) = ∞ ∫ −∞ Once the marginal distribution functions are known, it becomes simple to determine the conditional distribution functions. In many practical problems, we are interested in the distribution of the random variable X given that the random variable Y assumes some specific value, or that the random variable Y is between some interval from y1 to y2. When the random variable assumes some specific value, we say that we have point conditioning.

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