Test Academy | Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h(t) = y(t). Further, if |x(t)| * |h(t)| = z(t), which of the following statements is true? For all t ∈ (-∞, ∞), z(t) ≤ y(t), For some but not all t ∈ (-∞, ∞), z(t) ≤ y(t), For all t ∈ (-∞, ∞), z(t) ≥ y(t), For some but not all t ∈ (-∞, ∞), z(t) ≥ y(t)

Question

Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h(t) = y(t). Further, if |x(t)| * |h(t)| = z(t), which of the following statements is true?

Options :

For all t ∈ (-∞, ∞), z(t) ≤ y(t)
For some but not all t ∈ (-∞, ∞), z(t) ≤ y(t)
For all t ∈ (-∞, ∞), z(t) ≥ y(t)
For some but not all t ∈ (-∞, ∞), z(t) ≥ y(t)

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