# hwB33 - ENEE 241 02 HOMEWORK ASSIGNMENT 33 Due Fri 05/02...

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Unformatted text preview: ENEE 241 02* HOMEWORK ASSIGNMENT 33 Due Fri 05/02 Consider the FIR filter whose input-output relationship is given by y [ n ] = x [ n ]- 1 2 x [ n- 1] + 3 4 x [ n- 3]- 3 8 x [ n- 4] , n ∈ Z (i) Determine the response y ( i ) [ · ] of the filter to each of the input signals given by the equations below (valid for all n ∈ Z ). x (1) [ n ] = 2 n (2 pts.) x (2) [ n ] = 2- n (2 pts.) x (3) [ n ] = 3 · 2 n + 5 · 3 n (2 pts.) x (4) [ n ] = cos( πn/ 8 + 2 π/ 3) (3 pts.) x (5) [ n ] = 2- n · sin( πn/ 8 + 2 π/ 3) (4 pts.) (ii) (4 pts.) The FIR filter above (call it H 1 ) is connected in series (cascade) with another FIR filter H 2 , whose input-output relationship is y [ n ] = x [ n ] + x [ n- 1] + x [ n- 2] Determine the system function H ( z ) and the input-output relationship of the two-filter cascade H . (iii) (3 pts.) Suppose x [ n ] = 2 n is given as an input to the above two-filter cascade H . What is the output y [ n ]?...
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hwB33 - ENEE 241 02 HOMEWORK ASSIGNMENT 33 Due Fri 05/02...

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