I have a question. this is sub-question D:
Let $T\{x(t)\} = \int_{-\infty}^{t} [x(\tau) - x(\tau - 1)]d\tau$.
Consider the signal $x_3(t) = a_i, \forall t \in (i,i+1]$ and $\forall i \in \mathbb{Z}$.
Also, let $x_3(t)$ be a constant piecewise function.
Let $y_3(t) = T\{x_3(t)\} = t$.
Find the series $\{a_i\}_{i=-\infty}^{+\infty}$.
Assume that $T$ is a Linear Time-Invariant (LTI) system ( we proved it earlier )
Any tip will be welcomed, since I really don't how to start.
Tried maybe doing the definition of $y_3(t)$, but I reached nothing with this.
Tried also maybe turning the integral to series of integral with $a_i - a_{i-1}$, also did not work.