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[24 pts] Classify the following systems, with input $x(t)$ (or $x[n]$) and output $y(t)$ (or $y[n]$). In each column, write "yes", "no", or "?" if the property is not edcidable with the given information. (+1 for correct, 0 for blank, -0.5 for incorrect). (For 1d, you are given the system is known to be linear and time=invariant.) For 1b and 1d, 2 test input cases are given.
Let $\Pi(t) = u(t + \frac12) - u(t - \frac12)$.
System
Causal
Linear
Time-invariant
BIBO stable
a. $y(t) = 2x(t-1)-5$
yes
no
yes
yes
b. \begin{cases} x & \text{if input }x(t)=0 \ tu(t) & \text{if input }x(t)=u(t-1)\end{cases}
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