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ECE 220
Multimedia Signal Processing
Fall 2006
The Dirac Delta Function, Informally
The
Dirac delta function
(or
impulse function
, or
impulse
) is a particularly useful function of a
continuous variable that is employed frequently in signal processing. It is not a plain old vanilla
function as we are used to, but a
generalized function
(also called a
distribution
).
For good measure, the definition of a generalized function is given here:
Generalized
functions
are defined as continuous linear functionals over a space of infinitely differentiable
functions such that all continuous functions have derivatives which are themselves generalized
functions.
However, this is very abstract and memorizing it is not necessary to understand the
Dirac delta function. More important is understanding the properties of the function as given
below.
You will observe that the Dirac delta (which takes a continuous argument) has some
similarities to the Kronecker delta function (which takes a discrete argument). However, be
careful not to confuse the two! The Kronecker delta is a perfectly well behaved discretetime
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This note was uploaded on 02/10/2008 for the course ECE 2200 taught by Professor Johnson during the Fall '05 term at Cornell University (Engineering School).
 Fall '05
 JOHNSON
 Signal Processing

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