HW6Ans_2005

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

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Homework #Set 6 Discrete Fourier Transform 1. (a) ]. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 [ ] [ 1 = k X (b) ]. 5.0273i - 1 - 0 1.4966i - 1 - 0 0.6682i - 1 - 0 0.1989i - 1 - 0 0.1989i 1 - 0 0.6682i 1 - 0 1.4996i 1 - 0 5.0273i 1 - 8 [ ] [ 2 + + + + = k X (c) ]. 0 4.8284i 2 0 0 0 0.8284i 2 0 0 0 0.8284i - 2 0 0 0 4.8284i - 2 0 8 [ ] [ 4 + + = k X (d) ]. 0 0 0 4i 4 0 0 0 0 0 0 0 4i - 4 0 0 0 8 [ ] [ 4 + = k X (e) ]. 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 8 [ ] [ 5 = k X 2. ] 2 4 1 4 5 2 3 3 [ ] [ = n x (a) 32 ] 4 [ 8 ] [ ] [ ) 1 ( 7 0 8 7 0 8 = = = = = x k X e k X k k j k k π . (b) ]. 48 32 80 64 16 64 32 0 0 0 0 0 0 0 0 48 [ ] )) [(( 16 ])) [ ( DFT ( DFT 16 16 16 16 16 = = k x n x (c) 18 ] [ ) 1 ( ] 4 [ 7 0 8 = = = n n n x X . (d) 18 ] [ ) 1 ( ] 8 [ 15 0 16 = = = n n n x X . (e) 40 ] 3 [ 8 ] [ 11 ) 8 / 2 ( 7 0 8 = = = = x e k X n kn j k

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3. (a) ]. [ ] [ ] [ ] 1 8 [ ] [ 8 8 / 2 7 0 8 7 8 7 0 ) 1 8 ( 8 7 0 8 1 k X e W m x W W m x W n x k Y k j m km k m m k n k = = = = = = = π (b) () ]. )) 4 [(( ] [ ] [ ] [ 1 ] [ 8 8 7 0 ) 4 ( 8 7 0 8 4 8 7 0 8 2 ± = = = = = + = = k
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HW6Ans_2005 - Homework #Set 6 Discrete Fourier Transform 1....

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