Challenge06_z_transform

Challenge06_z_transform - [n The causal system has a...

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Digital Signal Processing Dr. Fred J. Taylor, Professor Lesson Title: z-Transform Lesson Number: 06 Challenge Problem Suppose a causal LTI system has an impulse response given by: [ ] = otherwise k n u n h n 0 0 ]; [ ) 9 . 0 ( In assembling the system, some logic is inverted and the system’s clock runs backwards in time (how this happened, I do no know), producing a new impulse response: h 0 [n]=h[-n]. What is the z-transform and ROC of the time-reversed anti-causal system h
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Unformatted text preview: [n]? The causal system has a z-transform given by: 9 . 9 . 1 1 ) 9 . ( ) ( 1-=-= =-∞ =-∑ z z z z z H n n n if |0.9z-1 |<1 or |z|>0.9 From Table 2, ( 29 z z z H z H 9 . 1 1 ) ( 9 . 1 1 ) / 1 ( ) ( 1 1-=-= =--From ( 29 ∑ ∞ = =-= = + + + = 2 2 9 . 1 1 ) 9 . ( ... ) 9 . ( ) 9 . ( 1 ) ( n n n z z z z z H which converges if |0.9z|<1 or |z|<1/0.9. 1...
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