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

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

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

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

$$y\left( n \right)$$ 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

each system in the cascade is individually casual and unstable

at least one system is unstable and atleast one system is casual

at least one system is casual and all systems are unstable

the majority are unstable and the majority are casual