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.9 KRONECKER DELTA FUNCTION
Definition: Kronecker Delta Function The Kronecker delta function is
(B.47) 
for 
.
Brackets are used so that the Kronecker delta function is not confused with the Dirac delta function. (The symbol δ k is also used for the Kronecker delta function; however, it is not used here because it resembles the Dirac measure discussed in Chapter 2.) It has the following basic properties:
(B.48) 
(B.49) 
for 
. The Kronecker delta function is convenient for defining probability mass functions (pmfs) and also for representing discrete-time signals and systems.
Definition: Kronecker Delta Function of Two Variables The two-dimensional Kronecker delta function is
(B.50) 
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