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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 ztransforms of the following functions along with their region of convergence. i. a n u [ n ] ii. a n u [n1] iii. n a n u [ n ] iv. z n (careful) Exercise 6. If X ( z ) is the ztransform of x [ n ] with ROC a <  z  < b , what are the ztransforms and ROCs of the following functions i. x [ nn ] 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 ztranform is given by X ( z ) = ( z 4 + 1)1 , with ROC  z  < 1 . 1...
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 Winter '08
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