2006-10-25 07:06:26 · 3 answers · asked by mohammad_rouhbakhsh 1 in Science & Mathematics ➔ Mathematics
The best explanation is given at the site below.
2006-10-25 07:21:14 · answer #1 · answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6 · 0⤊ 0⤋
The Dirac Delta Function is essentially an impulse. This is a pulse with area = 1. The amplitude of such a pulse is = a (for example), and the width of the pulse is = 1/a. For mathematical convenience this pulse (function) is defined as below:
d(t) = 1 (when t = 0)
= 0 (for all other values of t).
In solving the response of a Linear Time Invariant system to any arbitrary input signal, the Dirac Delta Functions (or Impulse Functions) are used. The arbitrary input signal is expressed as a linear weighted sum of impulses delayed appropriately. Then the response of the system to each individual impulse (or Dirac Delta Function) is determined.
By using principle of superposition then, the response of the system to the arbitrary signal is same as the response of the system to the sum of individual, weighted, shifted impulses.
This works because the arbitrary signal is expressed as a weighted, shifted linear sum of individual impulses (or Dirac Delta Functions).
Hope this helps.
2006-10-25 07:19:50 · answer #2 · answered by sanjayd_411 2 · 1⤊ 0⤋
dirac delta function : is a spike
+inf for t = 0
0 otherwise
It is used in the construction of digital filters.
2006-10-25 07:17:49 · answer #3 · answered by gjmb1960 7 · 0⤊ 0⤋