How can I plot this signal

Question

What will be the value of this signal (specified as impulse train) , say for values of t from 0 to 6 $$g(t)=\sum_{k=- \infty }^\infty \delta(t-2k)$$

Answer 1

The Dirac impulse $\delta(t)$ is a distribution and not a function in the usual sense. Its value at $t=0$ is not defined. However, $\delta(t)=0$ for $t\neq 0$. In your case, you have an impulse train, i.e. a sequence of impulses at $t=2k$, i.e. at points where $t$ is an even integer. So the impulse train has value $0$ almost everywhere except at points $t=2k$, where its value is not defined. Usually an impulse train is "plotted" like this:

In your case the distance between the impulses is $T=2$.

EDIT:

Judging from your comment you need the derivative of a signal which jumps up by a value of $3$ if $t$ is an even integer (i.e., $t=2k$) and which jumps down by $3$ if $t$ is an odd integer (i.e., $t=2k+1$). In this case the derivative is given by two impulse trains, on with impulses of area $3$ at $t=2k$, and one with impulse of area $-3$ at $t=2k+1$, i.e.

$$g(t)=3\sum_{k=-\infty}^{\infty}\delta(t-2k)-3\sum_{k=-\infty}^{\infty}\delta(t-2k-1)$$