Given a FIR filter with impulse response:
$$ h(n) = \begin{cases}1, &0 \leq n < 5\\ -1, &10 \leq n < 15 \\ 0, &\text{otherwise}\end{cases} $$
What would be the right approach to calculate the filter discrete unit step response?
I don’t understand..how can I apply convolution to these 2 functions? Especially since the impulse response is expressed in that way...
Hint:
For a discrete-time LTI system we have $$s[n] = \sum_{k = -\infty}^{n}h[k]$$And $$h[n] = s[n] - s[n-1]$$ Where $s[n]$ is the unit step response and $h[n]$ is the unit impulse response.