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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 $\left | x\left ( t \right ) \right |*\left | h\left ( t \right )\right |=z\left ( t \right )$,

which of the following statements is true?

  1. For all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\leq y\left ( t \right )$
  2. For some but not all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\leq y\left ( t \right )$
  3. For all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\geq y\left ( t \right )$
  4. For some but not all $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\geq y\left ( t \right )$
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