[PD] unit impulse without [dirac~]

Mathieu Bouchard matju at artengine.ca
Sun Nov 18 18:31:23 CET 2007

On Sat, 17 Nov 2007, Uur Güney wrote:

> When you let the bottom side's length of a triangle shaped function to 
> go to zero, for preserving its area, its height goes to infinity. Dirac 
> Delta Function is defined as this limiting case,

It can also be defined using any of a variety of functions of various 
shapes. You could do it by making a sequence of Gaussian distributions 
whose variances converge to zero, for example.

> (actually it is not a function, but a distribution. :-) Its behavoir is 
> very pathologic for a function. Distributions are more general.)

Yeah, you can actually write it as being the derivative of the step 
function, but you can't compute that derivative, as long as you need to 
stick with continuous functions, so you have to get rid of it 
algebraically, with some identities that make the nonsensical computations 

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| Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada

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