Question

(1) Memoryless (2) Time invariant (3) Linear (4) Casual (5) Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) denotes the system output and x(t) is the system input. (a) $y(t) = x(t - 2) + x(2 - t)$ (c) $y(t) = \int_{-\infty}^{2} x(\tau)d\tau$ (e) $y(t) = \begin{cases} 0, & x(t) < 0\\ x(t) + x(t - 2), & x(t) \ge 0 \end{cases}$ (g) $y(t) = \frac{dx(t)}{dt}$ (b) $y(t) = [cos(3t)]x(t)$ (d) $y(t) = \begin{cases} 0, & x(t) < 0\\ x(t) + x(t - 2), & x(t) \ge 0 \end{cases}$ (f) $y(t) = x(t/3)$

          (1) Memoryless
(2) Time invariant
(3) Linear
(4) Casual
(5) Stable
Determine which of these properties hold and which do not hold for each of the following
continuous-time systems. Justify your answers. In each example, y(t) denotes the system output
and x(t) is the system input.
(a) $y(t) = x(t - 2) + x(2 - t)$
(c) $y(t) = \int_{-\infty}^{2} x(\tau)d\tau$
(e) $y(t) = \begin{cases} 0, & x(t) < 0\\ x(t) + x(t - 2), & x(t) \ge 0 \end{cases}$
(g) $y(t) = \frac{dx(t)}{dt}$
(b) $y(t) = [cos(3t)]x(t)$
(d) $y(t) = \begin{cases} 0, & x(t) < 0\\ x(t) + x(t - 2), & x(t) \ge 0 \end{cases}$
(f) $y(t) = x(t/3)$

(1) Memoryless
(2) Time invariant
(3) Linear
(4) Casual
(5) Stable
Determine which of these properties hold and which do not hold for each of the following
continuous-time systems. Justify your answers. In each example, y(t) denotes the system output
and x(t) is the system input.
(a) y(t) = x(t - 2) + x(2 - t)
(c) y(t) = ∫-∞^2 x(τ)dτ
(e) y(t) = 0, x(t) < 0
x(t) + x(t - 2), x(t) ≥ 0
(g) y(t) = (dx(t))/(dt)
(b) y(t) = [cos(3t)]x(t)
(d) y(t) = 0, x(t) < 0
x(t) + x(t - 2), x(t) ≥ 0
(f) y(t) = x(t/3)

Added by Michele S.

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