[PD] unit impulse without [dirac~]

Uğur Güney ugurguney at gmail.com
Sat Nov 17 01:03:32 CET 2007

# What is preserved is the area under the function, it is equal to one (its
just 1, with no physical dimensions like energy. So, if x axis has the
dimensions of L(ength), y-axis has the dimension of 1/L). 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, other limiting case where the height goes to
zero and so length goes to infinity is unrelated to Dirac Delta Function.
(actually it is not a function, but a distribution. :-) Its behavoir is very
pathologic for a function. Distributions are more general.)
# The idea behind all of this cumbersome things become useful when you
multiply a function with Dirac Delta and take the integral:

integral{f(t)*delta(t-a)*dt} = f(a)

# So, Delta function takes a sample (a snapshot) from the function at time
# It can be used as a mathematical approximations of some real signals
(there can't be any physical quantity of which amplitude is infinity) or a
tool for solving problems.

On Nov 17, 2007 11:01 AM, Andy Farnell <padawan12 at obiwannabe.co.uk> wrote:

> Is it correct to say that the Dirac impulse preserves
> energy, as it tends towards zero time length the amplitude goes to
> infinity and if we
> squashed its amplitude to zero it would be infinitely long? In which case
> Dirac impulses
> are theoretical and not practical digital signals?
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