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Unformatted text preview: ENEE630 ADSP RECITATION 2 w/ solution September 17/18, 2009 1. Consider the structures shown in Fig. R2.1, with input transforms and filter responses as indicated. Sketch the quantities Y ( e jω ) and Y 1 ( e jω ). Figure R2.1: Solution: Comment: For a down-sampled signal, it’s still possible to recover the original signal (not necessarily low-pass) using filters and multirate building blocks as long as there is no aliasing ( H 1 in this problem). 2. For each case shown in the Fig. R2.2, prove or disprove whether the left system is equivalent to the right system? Assume M,L,K are all integers larger than 1. Solution: Assume the input, output, intermediate signals are x ( n ) ,y ( n ), and u ( n ), respectively. (a). (FD) U ( z ) = X ( z M ), Y 2 ( z ) = 1 M ∑ M- 1 k =0 U ( z 1 /M W k M ) = 1 M ∑ M- 1 k =0 X ( zW kM M ) = X ( z ). (TD) u ( n ) = x ( n M ) if n is a multiple of M , and u ( n ) = 0 otherwise. Then, y 2 ( n ) = u ( Mn ) = x ( n )....
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