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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 $x(t)\ast h(t)= y(t)$. Further, if $\mid x(t)\mid \ast \mid h(t)\mid = z(t) $, which of the following statements is true?

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