# 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 a.
# 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.
-uğur-

On Nov 17, 2007 11:01 AM, Andy Farnell <padawan12@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?