Infinite sum of heviside functions

[erezb84]

Homework Statement

how can i find the infinite sum of heviside functions?...

i have this func:
f(t) = sum[n=-infinity to infinity] (-1)^n*[u(t)-(u(t-T))]
where T is a period time..

 

[Ray Vickson]

Homework Statement

how can i find the infinite sum of heviside functions?...

i have this func:
f(t) = sum[n=-infinity to infinity] (-1)^n*[u(t)-(u(t-T))]
where T is a period time..

The notation is ambiguous. Do you mean $$f(t) = \sum_{n=-\infty}^{\infty} (-1)^n [u(t) - u(t-T)],$$ or do you mean $$f(t) = \sum_{n=-\infty}^{\infty} (-1)^{n [u(t) - u(t-T)]} ?$$ In any case, the function g(t) = u(t) - u(t-T) is 1 for 0 <= t < T and is zero for other values of t. That should allow you to easily examine your infinite series.

RGV