Chapter 9

Chapter 9 - CHAPTER 9 solutions 9.3 (a) 2-3x a[n] 8 6 4 2 0...

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Unformatted text preview: CHAPTER 9 solutions 9.3 (a) 2-3x a[n] 8 6 4 2 0 -2 -6 -4 -2 0 n 3x a[n-2] 2 4 6 0 -2 -4 -6 -4 -2 2 2x a[-n] 0 n 3-x a[n] 2 4 6 4 2 0 -2 -4 -6 -4 -2 0 2 4 n 1+2x a[n-2] 6 8 6 4 2 0 -6 -4 -2 0 n 2x a[-n]-4 2 4 6 4 2 0 -2 -4 -4 0 -2 -4 -6 -8 -2 0 2 n 4 6 8 -6 -4 -2 0 n 2 4 6 9.3 (b) 2-3x b[n] 5 5 0 0 -5 -4 -2 0 n 3x b[n-2] 2 4 6 -6 -4 -2 2x b[-n] -5 -6 0 n 3-x b[n] 2 4 6 6 5 4 0 2 -5 -4 -2 0 2 4 n 1+2x b[n-2] 6 8 0 -6 -4 -2 0 n 2x b[-n]-4 2 4 6 6 0 4 -2 2 0 -2 -8 -4 -4 -2 0 2 n 4 6 8 -6 -4 -2 0 n 2 4 6 -4 -6 9.3 (c) 2-3x c [n] 5 0 -5 -10 -6 -4 -2 0 n 3x c [n-2] 2 4 6 0 -5 -6 2x c [-n] 5 -4 -2 0 n 3-x c [n] 2 4 6 6 10 5 0 -5 -4 -2 0 2 n 1+2x c [n-2] 4 6 8 4 2 0 -2 -6 -4 -2 0 n 2x c [-n]-4 2 4 6 10 5 5 0 0 -4 -2 0 2 n 4 6 8 -5 -6 -4 -2 0 n 2 4 6 9.3 (d) 2-3x d[n] 2 0 -2 -4 -6 -8 -6 -4 -2 0 n 3x d[n-2] 2 4 6 0 -6 -4 -2 4 2 6 2x d[-n] 0 n 3-x d[n] 2 4 6 10 4 3 5 2 1 0 -4 -2 0 2 4 n 1+2x d[n-2] 6 8 0 -6 -4 -2 0 n 2x d[-n]-4 2 4 6 8 2 6 0 4 -2 2 -4 0 -4 -2 0 2 n 4 6 8 -6 -4 -2 0 n 2 4 6 9.4 (a) x a[-n]u[n] 2 1 0 -1 -2 -3 -6 2 1 0 -1 -2 -3 -6 x a[n]u[-n] -4 -2 0 n x a[n]u[n+2] 2 4 6 -4 -2 0 n x a[-n]u[-2-n] 2 4 6 2 1 0 -1 -2 -3 -6 2 1 0 -1 -2 -3 -6 -4 -2 0 n x a[n] δ [ n-2] 2 4 6 -4 -2 0 n 2 4 6 x a[n](δ [ n+1]-δ [ n-1]) 2 1 0 -1 -2 -3 -6 2 1 0 -1 -2 -3 -6 -4 -2 0 n 2 4 6 -4 -2 0 n 2 4 6 9.4 (b) x b[-n]u[n] 3 2 1 0 -1 -2 -3 -6 -4 -2 0 n x b[n]u[n+2] 3 2 1 0 -1 -2 -3 -6 -4 -2 0 n x b[n] δ [ n-2] 3 2 1 0 -1 -2 -3 -6 -4 -2 0 n 2 4 6 3 2 1 0 -1 -2 -3 -6 -4 -2 2 4 6 3 2 1 0 -1 -2 -3 -6 -4 -2 2 4 6 3 2 1 0 -1 -2 -3 -6 -4 -2 x b[n]u[-n] 0 n x b[-n]u[-2-n] 2 4 6 0 n 2 4 6 x b[n](δ [ n+1]-δ [ n-1]) 0 n 2 4 6 9.4 (c) x c [-n]u[n] 4 4 x c [n]u[-n] 2 2 0 0 -2 -6 -4 -2 0 n x c [n]u[n+2] 4 2 4 6 -2 -6 -4 -2 0 n x c [-n]u[-2-n] 4 2 4 6 2 2 0 0 -2 -6 -4 -2 0 n x c [n] δ [ n-2] 4 2 4 6 -2 -6 -4 -2 0 n 2 4 6 x c [n](δ [ n+1]-δ [ n-1]) 4 2 2 0 0 -2 -6 -4 -2 0 n 2 4 6 -2 -6 -4 -2 0 n 2 4 6 9.4 (d) x d[-n]u[n] 4 3 2 1 0 -6 4 3 2 1 0 -6 x d[n]u[-n] -4 -2 0 n x d[n]u[n+2] 2 4 6 -4 -2 0 n x d[-n]u[-2-n] 2 4 6 4 3 2 1 0 -6 4 3 2 1 0 -6 -4 -2 0 n x d[n] δ [ n-2] 2 4 6 -4 -2 0 n 2 4 6 x d[n](δ [ n+1]-δ [ n-1]) 4 3 2 1 0 -6 4 3 2 1 0 -6 -4 -2 0 n 2 4 6 -4 -2 0 n 2 4 6 9.5 9.8 x a,even[n] 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -6 -4 -2 0 n 2 4 6 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -6 -4 -2 0 n 2 4 6 x a,odd[n] x b,even[n] 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -6 -4 -2 0 n 2 4 6 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -6 -4 -2 x b,odd[n] 0 n 2 4 6 Continued 9.8, continued x c ,even[n] 5 4 3 2 1 0 -1 -2 -3 -6 -4 -2 0 n x d,even[n] 4 3 2 1 0 -1 -6 4 3 2 1 0 -1 -6 2 4 6 5 4 3 2 1 0 -1 -2 -3 -6 -4 -2 0 n x d,odd[n] 2 4 6 x c,odd[n] -4 -2 0 n 2 4 6 -4 -2 0 n 2 4 6 Continued 9.9, continued (b) x[n]=6u[n-3]: neither even nor odd 8 6 4 2 0 -6 5 x[n]=-n: odd 0 -5 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 x[n]=0.2|n|:even 1 0.8 0.6 0.4 50 0.2 0 -6 -4 -2 0 2 4 6 -3 -2 100 150 x[n]=6+0.2n+0.2-n:even -1 0 1 2 3 x[n]=sin(2n):odd 1.5 1 0.5 0 -0.5 -1 -1.5 -6 -4 -2 0 2 4 6 1.5 1 0.5 0 -0.5 -1 -1.5 -6 x[n]=sin(n-π/6):neither even nor odd -4 -2 0 2 4 6 Continued 9.9, continued even part of x[n]=6u[n-3] 4 3 2 1 0 -1 -2 -3 -4 -6 -4 -2 0 2 4 6 4 3 2 1 0 -1 -2 -3 -4 -6 -4 odd part of x[n]=6u[n-3] -2 0 2 4 6 even part of x[n]=sin(n-π/6) 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -6 -4 -2 0 2 4 6 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -6 -4 odd part of x[n]=sin(n-π/6) -2 0 2 4 6 Continued 9.23, continued Continued 9.23, continued Continued 9.25, continued Continued 9.27, continued continued 9.28, continued ...
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This note was uploaded on 06/10/2010 for the course ECES 302 taught by Professor Carr during the Spring '08 term at Drexel.

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