(Solved): Consider a causal filter whose input x[n] and output y[n] are related through the following differ ...

Consider a causal filter whose input $x[n]$ and output $y[n]$ are related through the following difference equation: $y[n]?0.25y[n?2]=x[n]+x[n?2]$ (a) Determine the impulse response of this filter by plugging in $?[n]$ for the input signal in the difference equation and solving for the output signal. (d) Determine whether or not this filter is stable by checking if the impulse response is absolutely summable. (b) Determine the z-transform of the impulse response of this filter and the location of its poles.