A linear time-invariant filter is described by the difference equation
y[n] = x[n] + 2 x[n – 1] + x[n – 2]
(a) Obtain an expression for the frequency response of this system.
(b) Sketch the frequency response (magnitude and phase) as a function of frequency.
(c) Determine the output when the input is x[n] = 10 + 4cos(0.5πn + π/4).
(d) Determine the output when the input is the unit- impulse sequence, δ[n].
(e) Determine the output when the input is the unit-step sequence, u[n].
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