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Unformatted text preview: F ( z ) = zN ˆ H ( z ) and F 1 ( z ) =H (z ) to get an aliasfree system, and check that T ( z ) = 1 2 zN using the result from part (c). Therefore, this is PR. Similarly, we can ﬁnd an aliasfree system when N is even; however, that system is not necessarily PR. Comment: As someone seems still confused about ˆ H , I’d like to clarify it by a simple example: Assume H ( z ) = az + bz 2 , then H * ( z ) = a * z + b * z 2 (only coeﬃcients), H * ( z ) = ( az + bz 2 ) * = a * z * + b * z * 2 (all), and H * ( z1 ) = a * z1 + b * z2 . 2...
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 Spring '10
 wu

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