An LTI 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(ejω), the frequency response of the system. Use trigonometric identities to obtain a simple expression for H(ejω).
(d) Plot the magnitude and phase of the frequency response.
(e) Now consider a new system whose frequency response is H1(ejω) = H(ej (ω+π)). Determine h1[n], the impulse response of the new system.
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