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# h218 - h n 6(15 Use MATLAB’s freqz command to plot the...

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Assignment #19 Fri 12/09/05 1(10). Find the z -transform of ( 29 ( 29 ] [ cos ] [ 4 3 1 n u n n x n π = , and sketch the pole-zero diagram of ) ( z X . (See Text, Example 10.4.) 2(20). Using tables 10.1 and 10.2, find the inverse z-transforms, 0 ], [ n n x , for (a) ( 29 ( 29 1 1 1 3 1 2 1 1 1 ) ( - - - + - - = z z z z X (b) 2 4 1 1 1 1 ) ( - - - - = z z z X (c) 2 1 3 ) ( - = - z z z X (d) 1 2 1 ) ( + + = z z z X 3(10) Find the inverse z-transform, 0 ], [ n n x , for 2 1 1 4 2 1 5 2 ) ( - - - + - - = z z z z X (Hint: Table 10.2, last two rows) 4(15). Text 10.33 (a), (b) 5(15). A discrete-time, linear, time-invariant system has output ( 29 ( 29 ] [ 1 ] [ 2 1 n u n y n - = when the input is a unit step. Using z -transforms, find the impulse response sequence,
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Unformatted text preview: h [ n ]. 6(15). Use MATLAB’s freqz command to plot the frequency response, ) ( ϖ j e X , 2 ≤ ≤ , for the pole-zero diagrams: 7(15). (a) Find the inverse z-transform of ( 29 2 1 2 1 2 1 1 1 ) (----= z z z X . Assume ] [ = n x for < n . (b) Use the initial value theorem to find ] [ x . Does this value agree with the result from part(a)? (c) Where are the poles of X ( z )? Is the sequence stable? (a) (b) (c)...
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