Hw4 P-6.14 - Problem 6.14(e) in SPF EEL 3135: Signals and...

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Unformatted text preview: Problem 6.14(e) in SPF EEL 3135: Signals and Systems G. Heitman Electrical and Computer Engineering University of Florida Spring 2006 ⎡ ⎛ π ⎞⎤ ⎛⎛ π ⎞⎞ x1 ( n) := ⎢5 + 4⋅ cos ⎜ ⎜ ⋅ n⎟ ⎟ + 3⋅ cos ⎜ ⋅ n⎟⎥ ⋅ Φ ( n) ⎣ ⎝⎝ 5 ⎠⎠ ⎝ 2 ⎠⎦ h ( n) := 1 ⋅ ( δ ( n , 0) + δ ( n , 1) ⋅ δ ( n , 2) + δ ( n , 3) ) 4 M := 3 ⎛ ⎛ L⋅ ω ⎞ ⎞ sin ⎜ ⎟ ⎜ ⎝ 2 ⎠⎟ D ( ω , L ) := if ⎜ ω = 0 , 1 , ⎟ ⎛ ω⎞⎟ ⎜ L⋅ sin ⎜ ⎟ ⎝ ⎝ 2 ⎠⎠ ⎛3⎞ H ( ω) := D ( ω , 4) ⋅ exp ⎜ −i⋅ ⋅ ω⎟ ⎝2⎠ ⎛ π ⎞ ⋅ cos ⎛ π ⋅ n + arg ⎛H ⎛ π ⎞⎞ ⎞ + 3⋅ H ⎛ π ⎞ ⋅ cos ⎛ π ⋅ n + arg ⎛ H ⎛ π ⎞ ⎞⎞ ⎟ ⎜ ⎜ ⎜ ⎟⎟⎟ ⎜⎟ ⎜ ⎜ ⎜ ⎟⎟⎟ ⎝ 5⎠ ⎝5 ⎝ ⎝ 5 ⎠⎠⎠ ⎝ 2⎠ ⎝2 ⎝ ⎝ 2 ⎠⎠⎠ yss ( n) := 5⋅ H ( 0) + 4⋅ H ⎜ y1 ( n) := 0 if n < 0 n ∑ ( h ( k) ⋅ x1 ( n − k) ) if 0 ≤ n < M k=0 yss ( n) if n ≥ M n := −4 .. 30 10 M y1( n) 5 yss ( n) 5 0 5 10 15 20 25 30 n EEL 3135 1 P-6.14.mcd ...
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