signal & zero

[logistic_guy]

Let $\displaystyle x[n]$ be a signal with $\displaystyle x[n] = 0$ for $\displaystyle n < -2$ and $\displaystyle n > 4$. For each signal given below, determine the values of $\displaystyle n$ for which it is guaranteed to be zero.

$\displaystyle \bold{(a)} \ x[n - 3]$
$\displaystyle \bold{(b)} \ x[n + 4]$
$\displaystyle \bold{(c)} \ x[-n]$
$\displaystyle \bold{(d)} \ x[-n + 2]$
$\displaystyle \bold{(e)} \ x[-n-2]$

 

[logistic_guy]

$\displaystyle \bold{(a)} \ x[n - 3]$

$\displaystyle x[n - 3] = 0$ for $\displaystyle n < 1$ and $\displaystyle n > 7$.

 

[logistic_guy]

$\displaystyle \bold{(b)} \ x[n + 4]$

$\displaystyle x[n + 4] = 0$ for $\displaystyle n < -6$ and $\displaystyle n > 0$