HW3Ans_2005

Digital Signal Processing: A Practical Approach (2nd Edition)

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Unformatted text preview: Homework #Set 3 Continuous to Discrete Time Translation 1. (a) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 3 2 cos 2 ] [ π n n x . (b) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 3 4 cos 2 ] [ π n n x . (c) ( ) 2 2 cos 2 ] [ = = π n n x . (d) ( ) 2 4 cos 2 ] [ = = π n n x . 2. (a) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 10 cos 5 2 sin ] [ π π n n n x . (b) ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 4 cos 4 cos sin ] [ π π π n n n n x . (c) ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 2 cos 2 cos 2 sin ] [ π π π n n n n x . (d) ( ) ( ) n n n n x ) 1 ( cos 4 sin ] [ − = + = π π . 3. (a) Y (b) Y (c) Y (d) N (Not bandlimited in π /2) (e) Y ( sin( π n)=0 ) 4. (a) ⎩ ⎨ ⎧ > Ω ≤ Ω = Ω π π k k j H a 16 , 16 , 1 ) ( ⎪ ⎩ ⎪ ⎨ ⎧ > ≤ = π π k w k w k jw H b 16 , 16 , 16 1 ) ( (b) Simple antialiasing filter C/D Sharp antialiasing Filter cutoff = 6 x c ( t ) x d [ n ] Sampling rate reduction by 6 6x16 kHz 6 / π ) ( Ω j H aa ) ( ω j e H ) ( t x a ] [...
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HW3Ans_2005 - Homework #Set 3 Continuous to Discrete Time...

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