Dirac_delta.220.06 - ECE 220 Multimedia Signal Processing Fall 2006 The Dirac Delta Function Informally The Dirac delta function(or impulse

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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 discrete-time
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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).

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Dirac_delta.220.06 - ECE 220 Multimedia Signal Processing Fall 2006 The Dirac Delta Function Informally The Dirac delta function(or impulse

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