hw18 - 6. (a) Starting with the transfer function for a 2...

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Assignment #18 Tue 11/06/05 1. Text 9.64 2. What is the required order for a Butterworth low-pass filter if the gain must be -20 dB at c ϖ 2 = ? Remember, n must be an integer. 3. Sketch the straight-line Bode magnitude diagram for a 3 rd order Butterworth low-pass filter with 1 = c . Remember, Bode diagrams are drawn on a semi-log scale. Verify your sketch by plotting the exact magnitude frequency response using MATLAB. Superimpose the straight-line plot on the MATLAB generated plot. 4. Find the transfer function ) ( s B for a 3 rd order Butterworth low-pass filter with bandwidth = 4 kHz. 5. (a) Design a Butterworth low-pass filter that meets the following specifications: ( i ) the absolute magnitude is between 1 and 0.794 in the frequency range 10 0 . ( ii ) the absolute magnitude is less than 0.1 for 20 . i.e ., find the order, n and bandwidth, c . (b) Use MATLAB to plot your result. Verify from your plot that your design meets the criteria above.
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Unformatted text preview: 6. (a) Starting with the transfer function for a 2 nd order Butterworth prototype filter, ) ( s B , find the transfer function for a Butterworth band-pass filter, ) ( s H BP , with cutoff frequencies of 90 and 120 rad/sec. (b) Plot . . ) ( s v H BP using MATLAB. 7. Find the z-transform of (a) ( 29 ] 3 [ ] [ 5 1-= n u n x n , by solving the defining summation formula. (b) ( 29 ] 2 [ ] [ 1 2 1-=-n u n x n , by using the table and properties. 8. Find the z-transform for the following repeating, infinite, sequences for n , when x [ n ]=0, < n : Note. It is possible to write a sequence as a combination of simpler ones. See Videos. (a) ,...} 1 , , , , 1 , , , , 1 { ] [ = n x a (b) ,...} , , 1 , 1 , , , 1 , 1 { ] [ = n x b (c) ,...} 1 , 1 , 2 , 2 , 1 , 1 , 2 , 2 { ] [ = n x c ....
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