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Unformatted text preview: -2] = 2 x [ n ] . i. Find the impulse response if the system is known to be causal. ii. Find the impulse response if the system is known to be stable. iii. Can the system be both causal and stable at the same time? Justify your answer. Exercise 5. Find the z-transforms of the following functions along with their region of conver-gence. i. a n u [ n ] ii. a n u [-n-1] iii. n a n u [ n ] iv. z n (careful) Exercise 6. If X ( z ) is the z-transform of x [ n ] with ROC a < | z | < b , what are the z-transforms and ROCs of the following functions i. x [ n-n ] ii. x [-n ] iii. z n x [ n ] iv. n x [ n ] Justify all your answers. Exercise 7. Find the discrete signal x [ n ] , whose z-tranform is given by X ( z ) = ( z 4 + 1)-1 , with ROC | z | < 1 . 1...
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- Winter '08