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 \(\displaystyle n > 0\)

 

[logistic_guy]

\(\displaystyle \bold{(c)} \ x[-n]\)

\(\displaystyle x[-n] = 0\) for \(\displaystyle n < -4\) and \(\displaystyle n > 2\)

 

[logistic_guy]

\(\displaystyle \bold{(d)} \ x[-n + 2]\)

\(\displaystyle x[-n + 2] = 0\) for \(\displaystyle n < -2\) and \(\displaystyle n > 4\)

 

[logistic_guy]

\(\displaystyle \bold{(e)} \ x[-n-2]\)

\(\displaystyle x[-n-2] = 0\) for \(\displaystyle n < -6\) and \(\displaystyle n > 0\)