hw3sol - j ω = 1 expressible in form 8(a h[n = ¼ δ[n-1...

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ECE 220 Spring 2005 Homework 3 Solutions 1. (a) y[n] = 2x[n-1] + 4x[n-2] – x[n-4] (b) direct form (c) transposed direct form 2. (a) n 0 1 2 3 4 5 6 7 8 9 10 y[n] 0 5 20 7 3 -1 -4 2 2 2 2 (b) h[n] = 5 δ [n] - 3 δ [n-2] 3. (a) linear, not time invariant, causal (b) linear, time invariant, causal (c) not linear, time invariant, causal (d) linear, time invariant, not causal 4. y[n] = δ [n] + δ [n-1] - δ [n-2] - δ [n-3] 5. (a) x[n] = δ [n-1] + δ [n-2] + δ [n-3] (b) h[n] = δ [n] - δ [n-1]
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6. (a) y[n] = 1/3( δ [n] - δ [n-1] + δ [n-2] - δ [n-3] + δ [n-4] - δ [n-5]) (b) y[n] = 1/3(x[n] + x[n-2] + x[n-4]) 7. (a) B = 2Asin( ω /2) θ = φ - ω /2 + π /2 ω = ϖ (b) not expressible in form (c) let H(e
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