These weighted-impulse-response $\displaystyle h$ coefficients (should) represent a differentiator:

$\displaystyle h = \frac{1}{3}(-1, -2, 0, 2, 1)$If $\displaystyle x[n]$ is the input sample, what is then the output $\displaystyle y[n]$?

Is it this: $\displaystyle y[n] = \frac{1}{3}\big(-x[n-4] - 2x[n-3] + x[n-1] + 2x[n]\big)$ ?

Thank you.