Fourier analysis: Impulse Symbol(dirac Delta Function)

[ryng35]

1. what is the even part of δ(x+3)+δ(x+2) -δ(x+1) +1/2δ(x) +δ(x-1) -δ(x-2) -δ(x-3)?


2. δ= 0 x≠0; ∞ x = 0
1/2 (f(x) + f(-x))
1/2 (f(x) - f(-x))



Knowing the piecewise definition of the delta function, and knowing 1/2 (f(x) + f(-x)) for even parts of a function. I plug this in, knowing that it will give me delta function to be even. I am not sure of exactly how to approach this problem? any help will be greatly appreciated

 

[ryng35]

It clicked on me last night, while I was thinking about this. I think the way I should approach this problem is not to find out a value per-say of the even part, but to look at this problem graphically. By looking at the graph of the function, I can graph the different spikes then find the "even part" graphically.