November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
Content preview from Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
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D.7 DOUBLE INTEGRALS OF SPECIAL FUNCTIONS
Finally, we summarize some double integrals of a few special functions of two variables. They include 
, u(x−y), min(x, y), max(x, y), and |x−y|. Some of these are useful in Chapter 7 on mean-square calculus where the autocorrelation function RXX(t1, t2) for nonstationary random process X(t) is integrated. All the results depend on which upper limit is larger.
FIGURE D.6 Integrals of 
and u(y−x). (a) 
. (b) 
. This is also 
and corresponds to min(x, y). (c) 
. (Note scale change from (b) to (c).)
- Dirac delta function
. This function is nonzero on the x–y-plane for all x = y. When it is integrated over y, unit-step functions are obtained along the line ...
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