What is the strength of a delta function.

Click For Summary
The strength of a delta function is indicated by its coefficient, which represents the area under the curve. In the discussion, the delta function's strength is described as Y/2, suggesting that g(t) can be expressed as 0.5Yδ(t). This formulation implies that the integral of g(t) over all time equals Y/2. Thus, the delta function's strength directly correlates with the integral value. Understanding this relationship is crucial for analyzing functions involving delta functions in mathematical contexts.
jk_zhengli
Messages
6
Reaction score
0
Hi all,

I read the following:

"If g(t) starts with a delta function of strength Y/2, then..."

I wonder what that means. Does it mean g(t) = 0.5Yδ(t) ?

Thanks
 
Physics news on Phys.org
Yes. It means that

\int_{-\infty}^{+\infty} g(t)dt=\frac{Y}{2}

So it coincides with \frac{Y}{2}\delta (t).
 

Similar threads

Undergrad Exercise 2.23 in Folland's real analysis text
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Distributions (generalised functions) basics
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad How Does Fourier Transform Analyze Beats in Signals?
  • · Replies 7 ·
Replies
7
Views
3K
Covariant derivative acting on Dirac delta function in curved space
  • · Replies 0 ·
Replies
0
Views
2K
MHB How can we compare the lower envelope of a function with the function itself?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Continuity of an inverse of a function
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Showing that a function is analytic
  • · Replies 2 ·
Replies
2
Views
2K
Insights What Exactly is Dirac’s Delta Function? - Insight
  • · Replies 33 ·
2
Replies
33
Views
6K
MHB Understanding Theorem 3.4: Mean Value Theorem & Cauchy Riemann Equations
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Intermediate Value Theorem .... Browder, Theorem 3.16 .... ....
  • · Replies 4 ·
Replies
4
Views
2K