a) Denote the input signal by x[n] and the output signal by y[n]. Find the difference equations for the filter.
f) Find the impulse response of the system. (Eliminate j (the imaginary unit) from your answer.)
I used the partial fractions method and obtained the following solution.
However it was time consuming. Is there a way that I can simplify this difference equation to get the impulse response of the IIR filter to get the same solution. Any help will be appreciated(as I am not aware of solving by difference equations)