A linear time-invariant system is described by the input-output relation 

y[n] = x[n] + 2x[n – 1] + x[n – 2]

(a) Determine h[n], the impulse response of the system. 

(b) Is this a stable system?

(c) Determine H(e^jω), the frequency response of the system. Use trigonometric identities to obtain a simple expression for H(e^jω).

(d) Plot the magnitude and phase of the frequency response.

(e) Now consider a new system whose frequency response is H₁(e^jω) = H(e^{j(ω + π)}). Determine h₁[n], the impulse response of the new system.