1.27. In this chapter, we introduced a number of general properties of systems. In partic- ular, a system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (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) de- notes the system output and x(t) is the system input. 0, (d) y(t) { 1²0 = x(t) + x(t2), (g) y(t) = dx(t) dt

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1.27. In this chapter, we introduced a number of general properties of systems. In partic-
ular, a system may or may not be
(1) Memoryless
(2) Time invariant
(3) Linear
(4) Causal
(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) de-
notes the system output and x(t) is the system input.
(d) y(t)
=
(g) y(t)
0,
x(t) + x(t − 2),
=
dx(t)
dt
t < 0
t> 0
Note do NOT use synthetic multiplication
to solve convolution problems. You can
check with this but you must demonstrate
the other processes.
Transcribed Image Text:1.27. In this chapter, we introduced a number of general properties of systems. In partic- ular, a system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (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) de- notes the system output and x(t) is the system input. (d) y(t) = (g) y(t) 0, x(t) + x(t − 2), = dx(t) dt t < 0 t> 0 Note do NOT use synthetic multiplication to solve convolution problems. You can check with this but you must demonstrate the other processes.
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