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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B.12 TRIANGLE AND RAMP FUNCTIONS
Definition: Triangle Function The triangle function is
(B.60) 
The symbol 
is sometimes used.
The rectangle function is used above to specify the support of tri(x), by appropriately truncating 1−|x|. The triangle function can be derived by convolving two rectangle functions:
(B.61) 
Definition: Ramp Function The ramp function is
(B.62) 
The unit-step function in the second expression defines the support of R(x) by truncating the linear function g(x) = x. The ramp function is obtained by integrating the unit-step function:
(B.63) 
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