A discrete-time IIR system is represented by the following difference equation y[n] = 0.15y[n−2]+x[n], n ≥ 0 where x[n] is the input and y[n] is the output.

(a) To find the impulse response h[n] of the system, let x[n] = δ[n], y[n] = h[n], and the initial conditions be zero. Find recursively the values of h[n] for values of n ≥ 0.

(b) As a second way to find h[n], replace the relation between the input and the output given by the difference equation to obtain a convolution sum representation which will give the impulse response h[n]. What is h[n]?

(c) Use the MATLAB function filter to get the impulse response h[n] (use help to learn about the function filter).