# Delta function

Can someone explain to me why in this equation (attached)

where ρ(t)=$\sum$δ(t-ti) , dirac funtion.
in the left side we have the sum over h(t-ti) instead of the sum over h(ti) ?

It seems to me that the integral would work summing 1*h(t1)+1*h(t2)+...+1*h(ti) for all ti smaller than t.

Last edited:

Fredrik
Staff Emeritus
Gold Member
$$\int\mathrm d\tau\, h(\tau)\rho(t-\tau) =\int\mathrm d\tau\, h(\tau)\sum_i\delta((t-\tau)-t_i) =\sum_i\int\mathrm d\tau\, h(\tau)\delta(\tau-(t-t_i)) =\sum_i h(t-t_i)$$

Thanks, one more question, what does tau stands for in this type of integral. i.e. What is the meaning of (t-tau)?

Last edited:
Fredrik
Staff Emeritus