3. Consider the system defined by the difference equation

2y[n] -0.5y[n 1] = x[n]

(a) sketch an implementation of the system

(b) determine and sketch the impulse response of the system

(c) determine and sketch few samples of the response of the system to the input

i. recursively

ii. via the convolution sum

n-5

x[n] = (u(n − 5)

-

(1)