11.8 Let x[n] = u[n+ 2] − u[n − 3] (a) Find the DTFT X(e) of x[n] and sketch |X(e)|vs w giving its value at w = ±, ±π/2,

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11.8 Let x[n] = u[n+ 2] − u[n − 3] (a) Find the DTFT X(e) of x[n] and sketch |X(e)|vs w giving its value at w = ±, ±π/2, 0. (b) If x₁ [n] = x[2n], i.e., x[n] is down-sampled with M = 2, find its DTFT X₁ (e). Carefully sketch x₁ [n] and X₁ (e)| indicating its values at w = ±, ±л/2, 0. Is X₁ (e) 0.5X(e/2)? If not, how would you process x[n] so that when x₁ [n] = x[2n] you would satisfy this condition? Explain. = (c) Consider now the up-sampled signal x[n/2] n even x₂ [n] = otherwise Find the DTFT X₂(e) of x₂ [n], and carefully sketch both (in particular, when plotting X₂ (¹) indicate the values at frequencies w = ±, ±л/2,0). Explain the differences between this case the down-sampling cases.