Suppose for input $x(t)$ a linear time-invariant system with impulse response $h(t)$ produces output $y(t)$,so that $x\left ( t \right )*h\left ( t \right )=y\left ( t \right )$. Further, if $\mid x\left ( t \right ) \mid *\mid h\left ( t \right )\mid =z\left ( t \right )$, which of the following statements is true?
- For all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\leq y\left ( t \right )$
- For some but not all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\leq y\left ( t \right )$
- For all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\geq y\left ( t \right )$
- For some but not all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\geq y\left ( t \right )$