Determining whether or not a system is BIBO stable I'm trying to determine whether or not a system with impulse response

$$
h(t) = \sum_{n=-\infty}^{\infty} \delta(t-2n)
$$

is BIBO stable. I haven't touched this material for a very long time -- could anyone lend a helping hand? I recall needing to show that

$$
\int_{-\infty}^{\infty} |h(t)| \, dt &lt; \infty,
$$

but $h(t)$ is defined in a very weird way, and calculating the integral is proving to be difficult.



EDIT: Does the following argument seem reasonable? Since were summing an infinite number of $\delta$ functions, each will have an argument of $0$ for some unique value of $t$. Thus, there are infinitely many values of $t$ for which $\delta(t-2n)=1$, so the integral diverges.
In your case

$$\int_{-\infty}^{\infty}|h(t)|dt=\int_{-\infty}^{\infty}h(t)dt=
\int_{-\infty}^{\infty}\sum_{n=-\infty}^{\infty}\delta(t-2n)dt=
\sum_{n=-\infty}^{\infty}\int_{-\infty}^{\infty}\delta(t-2n)dt$$

And since

$$\int_{-\infty}^{\infty}\delta(t-2n)dt=1$$

(as correctly pointed out by Dilip Sarwate in his comment to Phonon's answer), the above sum is

$$\sum_{n=-\infty}^{\infty}1=1+1+1+\ldots=\infty$$

I believe that this is basically the argument you gave in your question.