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hwB37 - ENEE 241 02 HOMEWORK ASSIGNMENT 37 Due Mon 05/12 A...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 37 Due Mon 05/12 A FIR filter acts on the input sequence given by x [0 : 5] = £ 1 - 3 5 - 2 6 2 / T ; x [ n ] = 0 for n < 0 and n > 5 to produce the output sequence given by y [0 : 11] = £ 2 - 3 0 10 23 - 27 61 - 51 54 14 - 2 / T and y [ n ] = 0 for n < 0 and n > 11. (i) (2 pts.) What is the length of the filter coefficient vector b ? (As usual, it is assumed that the first and last entries in b are nonzero.) (ii) (6 pts.) Use the FFT command in MATLAB to determine the coefficient vector b . (Alterna- tively, b can be determined by solving a triangular system of linear equations.) (iii) (6 pts.) Without performing a convolution, determine the response of the filter to the input sequence x (1) [ · ] whose nonzero entries are x (1) [0 : 11] = £ 1 - 3 5 - 2 6 2 1 - 3 5 - 2 6 2 / T (iv) (6 pts.) Without performing a convolution, determine the response of the filter to the input sequence x (2) [ · ] whose nonzero entries are x (2) [0 : 9] = £ 2 - 6 10 - 4 11 7 - 5 2 - 6 - 2 / T Solved Examples S 37.1 ( P 4.21 in textbook). Consider the FIR filter y [ n ] = x [ n ] - 2 x [ n - 1] - x [ n - 2] + 4 x [ n - 3] - x [ n - 4] - 2 x [ n - 5] + x [ n - 6]

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hwB37 - ENEE 241 02 HOMEWORK ASSIGNMENT 37 Due Mon 05/12 A...

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