A#22 - -= when the input is a unit step, x [ n ]= u [ n ]....

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Assignment #22 Due Fri 12/8/06 1(20). A first-order, recursive, digital lowpass filter is described by ] 1 [ 6 1 ] [ 3 1 ] 1 [ 2 1 ] [ - + = - - n x n x n y n y . (a) Find the transfer function ) ( z H of the lowpass filter. (b) Find the impulse response of the lowpass filter using z -transforms. (c) Find the step response of the lowpass filter using z -transforms. (d) Plot the pole-zero diagram of H ( z ) in the z -plane. (d) Is the lowpass filter stable? Why or why not? 2(20). The output of a discrete-time linear, time-invariant system is ] [ 2 1 1 ] [ n u n y n
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Unformatted text preview: -= when the input is a unit step, x [ n ]= u [ n ]. Using z-transforms, find the impulse response, h [ n ]. 3(20). Find the inverse transform of ( 29 +-+- =---2 1 1 16 1 4 1 1 3 2 1 8 4 1 ) ( z z z z X . 4(20). Find Find the inverse transform of ( 29 +--=---2 1 1 8 . 6 . 1 1 1 5 ) ( z z z z X . 5(20). Find the inverse transform of ( 29 ) 25 6 1 )( 1 ( 17 3 2 ) ( 2 1 1 1 1-----+--+ = z z z z z z X ....
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