$$3$$ and $$4$$

$$2$$ and $$3$$

$$1$$ and $$2$$

$$1,2$$ and $$4$$

$$y\left( t \right)$$

$$y\left( {2\left( {t - \tau } \right)} \right)$$

$$y\left( {t - \tau } \right)$$

$$y\left( {t - 2\tau } \right)$$

$$y\left( n \right)$$ is non causal with finite support

$$y\left( n \right)$$ is causal with infinite support

$$y\left( n \right)$$ $$ = 0;\,|n| > 3$$

$$\eqalign{ & {\mathop{\rm Re}\nolimits} {\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}} = - {\mathop{\rm Re}\nolimits} {\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}}; \cr & {\rm I}m{\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}}\, = {\rm I}m{\left[ {Y\left( z \right)} \right]_z} = {e^{j0}};\,\, - \pi \le \theta < \pi \cr} $$

$$x(t)$$ has finite energy because only finitely many coefficients are non $$-$$ zero

$$x(t)$$ has zero average value because it is periodic

the imaginary part of $$x(t)$$ is constant

The real part of $$x(t)$$ is even