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Unformatted text preview: F ( z ) = z-N ˆ H ( z ) and F 1 ( z ) =-H (-z ) to get an alias-free system, and check that T ( z ) = 1 2 z-N using the result from part (c). Therefore, this is PR. Similarly, we can ﬁnd an alias-free 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 * ( z-1 ) = a * z-1 + b * z-2 . 2...
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- Spring '10