Exam 2 Solution Spring 209

1 a e j 2 kd 1 c 2k 1 j j c 0 c j j sinm

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Unformatted text preview: < 1/ kD 1 n a uŒn .jaj < 1/ 1 1 e j! uŒn C n .n C 1/a uŒn .jaj < 1/ sin.!c n/ n xŒn D ( X.e j! / D 1 0nM 0 otherwise 2ı.! C 2k/ 1 1a P1 e j! k D 1 ı.! 1 .1 ( a e j ! /2 kD 1 C 2k/ 1 j! j < ! c 0 ! c < j! j   sinŒ!.M C1/=2 e sin.!=2/ P1 e j!0 n j ! n0 2ı.! j !M=2 !0 C 2k/ Common z-transform pairs Sequence Transform ROC ıŒn 1 All z uŒn 1 1z1 1 1z1 m jz j > 1 uŒ n ıŒn 1 m z 1 1 az 1 1 1 az 1 az 1 .1 az 1 /2 az 1 .1 az 1 /2 an uŒn n a uŒ n 1 n na uŒn n n a uŒ n ( an 0 1 0nN otherwise cos.!0 n/uŒn r n cos.!0 n/uŒn 1; 1 aN z N 1 az 1 1 cos.!0 /z 1 1 2 cos.!0 /z 1 Cz 2 1 r cos.!0 /z 1 1 2r cos.!0 /z 1 Cr 2 z 2 jz j < 1 All z except 0 or 1 jz j > ja j jz j < ja j jz j > ja j jz j < ja j jz j > 0 jz j > 1 jz j > r...
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This note was uploaded on 11/14/2013 for the course EEE 4001F taught by Professor Nicolls during the Summer '13 term at University of Cape Town.

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