A#21 - (c) x c [ n ]={0 ,0,1,1,0,0,1,1,. ..}. 4(25). A...

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Assignment #21 ECSE-2410 Signals & Systems - Spring 2007 Fri 04/27/07 1(10). The signal x ( t )=cos(5 π t ) is sampled every 0.1 seconds, starting at t =0. Find X ( z ), the z -transform of the resulting sampled signal x [ n ]. Note that x [ n ]=0 for n <0. 2(15). a.) (5) Find the z -transform of the signal x [ n ] given by x [-1] = 1, x [0] = 5, x [1] = 2 and x [ n ] = 0 for all other values of n . b.) (5) Find the signal h [ n ] whose z -transform is . z + z 0.1 + 5 = H(z) -3 -1 c.) (5) Use z -transforms to find ) ( ) ( z X z H h[n] * x[n] = y[n] . Note: this should explain how the convolution array works and why the MatLab conv can be used to multiply two polynomials. 3(30). Find the z -transform, X ( z ), of the following repeating sequences: (a) x a [ n ]={1 ,0,1,0,1,0,. ..} (b) x b [ n ]={2 ,1,2,1,2,1,2,1,0,. ..} You should be able to use the results from part (a).
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Unformatted text preview: (c) x c [ n ]={0 ,0,1,1,0,0,1,1,. ..}. 4(25). A first-order, recursive, digital lowpass filter is described by ] 1 [ 3 1 ] [ 2 1 ] 1 [ 2 1 ] [ + = n x n x n y n y . (a) Find the transfer function of the lowpass filter. ) ( z H (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. (e) Is the lowpass filter stable? Why or why not? 5(20). Find the closed form analytic expressions for the inverse z-transforms of the following. Use tables and properties. (a) 2 4 1 1 1 1 ) ( = z z z X a (b) ( ) ( ) 1/-z z z = (z) X 1--b 2 1 1 2...
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