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F09_630_rec_4_sol

# F09_630_rec_4_sol - ENEE630 ADSP 1 RECITATION 4 w solution...

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ENEE630 ADSP RECITATION 4 w/ solution October 1/2, 2009 1. Find the efficient structure for fractional decimation in Fig. R4.1, with H ( z ) = 10 X n =0 nz - n . Please first apply the Type 1 polyphase decomposition. Illustrate your implementation. Figure R4.1: Solution: The intermediate block diagram is shown in the left figure, and the final result is on the right. The polyphase components are as follows, E 0 ( z ) = 3 z - 1 + 6 z - 2 + 9 z - 3 , E 1 ( z ) = 1 + 4 z - 1 + 7 z - 2 + 10 z - 3 , E 2 ( z ) = 2 + 5 z - 1 + 8 z - 2 . E 00 ( z ) = 3 + 9 z - 1 , E 01 ( z ) = 6 z - 1 , E 10 ( z ) = 4 + 10 z - 1 , E 11 ( z ) = 1 + 7 z - 1 , E 20 ( z ) = 5 z - 1 , E 21 ( z ) = 2 + 8 z - 1 . Note: For this problem, the solution is not unique. For instance, in recitation we used the trick z - 2 = z 4 z - 6 when dealing with the third branch. However, since z - 2 can directly interchange the order with the upsampler, the following intermediate block diagram is also correct. 2. Prove that the block diagram shown in Fig. R4.2(a) is a perfect reconstruction system. Based on this, answer the following questions (No knowledge of QMF bank is needed though. We will

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F09_630_rec_4_sol - ENEE630 ADSP 1 RECITATION 4 w solution...

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