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
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B.11 RECTANGLE FUNCTIONS
Definition: Rectangle Function The rectangle function is
(B.56) 
The symbol 
is sometimes used.
It can be written in terms of the unit-step function as follows:
(B.57) 
We have arbitrarily defined 
since the Lebesgue measure of 
is zero, although it is possible to assign zero to 
. Another definition assigns 1/2 to 
:
(B.58) 
This last form is consistent with the definition of the signum function, so that sgn(x) can be written in terms of rect(x) by appropriate scaling and shifting. The rectangle function based on the first definition is often used to specify the support of a function (see the triangle function below).
Definition: Discrete Rectangle Function The discrete ...
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