hw3sol - j ) = 1, expressible in form 8. (a) h[n] = ( [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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Unformatted text preview: j ) = 1, expressible in form 8. (a) h[n] = ( [n-1] + [n-1] + [n-2] + [n-3]) (b) H(e j ) = e-j3 /2 [cos(1.5 ) + cos(0.5 )] (c) (d) y[n] = 5 + 3.076cos(0.2 n 0.3 ) (e) filter is length 4, so for n 3 9. y(t) = 10 + 6.152cos(200 t 0.3 ) 10. (a) y[n] = y 1 [n] because DC value is removed by filter (b) H(e j ) = 2/3e-j(3 /2- /2) sin(1.5 ) (c) see next page (c) (d) y[n] = 1/3x[n] 1/3x[n-3] 11. (a) y[n] = 10 + 9cos(0.2 n - /2) (b) at = 2 0.17: phase is wrapped to plot between [- ] at = : amplitude of H(e j ) changes sign, therefore phase jump...
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This homework help was uploaded on 10/10/2007 for the course ECE 2200 taught by Professor Johnson during the Spring '05 term at Cornell University (Engineering School).

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hw3sol - j ) = 1, expressible in form 8. (a) h[n] = ( [n-1]...

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